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Hidden Consequence Of Active Local Lorentz Invariance
No full textIn this paper we investigate a hidden consequence of the hypothesis that Lagrangians and field equations must be invariant under active local Lorentz transformations. We show that this hypothesis implies in an equivalence between spacetime structures with several curvature and torsion possibilities. © 2006 World Scientific Publishing Company.22305357Aharonov, Y., Susskind, L., Observality of the sign of spinors under a 2π rotation (1967) Phys. Rev., 158, pp. 1237-1238Bleecker, D., (1981) Gauge Theory and Variational Principles, , (Addison-Wesley Publ. Co., Inc., Reading, MA)Choquet-Bruhat, Y., DeWitt-Morette, C., Dillard-Bleick, M., (1977) Analysis, Manifolds and Physics, , revised edn. (North-Holland Publ. Co, Amsterdam)Crumeyrolle, A., (1990) Orthogonal and Sympletic Clifford Algebras, , (Kluwer Acad. Publ., Dordrecht)Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Euclidean Clifford algebra (2001) Adv. Appl. Clifford Algebras, 11 (S3), pp. 1-21Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., (2001) Extensors, Adv. Appl. Clifford Algebras, 11 (S3), pp. 23-40Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Metric tensor vs. metric extensor (2001) Adv. Appl. Clifford Algebras, 11 (S3), pp. 41-48Geroch, R., Spinor structure of spacetimes in general relativity. I (1988) J. Math. Phys., 9, pp. 1739-1744Hehl, F.W., Datta, B.K., Nonlinear spinor equation and asymmetric conection in general relativity (1967) J. Math. Phys., 12, pp. 798-808Ivanenko, D.D., Landau, L.D., Zur theorie des magnetischen elektrons (1928) I, Z. Phys., 48, pp. 340-348Kobayashi, S., Nomizu, K., (1963) Foundations of Differential Geometry, 1. , (Interscience Publishers, New York)Lawson Blaine Jr., H., Michelson, M.L., (1989) Spin Geometry, , (Princeton University Press, Princeton)Mielke, E.W., (1987) Geometrodynamics of Gauge Fields, , (Akademie-Verlag, Berlin)Mosna, R.A., Rodrigues Jr., W.A., The bundles of algebraic and Dirac-Hestenes spinor fields (2004) J. Math. Phys., 45, pp. 2945-2966Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Lagrangian formalism for multivector fields on spacetime (2001) Int. J. Theor. Phys., 40, pp. 299-313Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Metric Clifford algebra (2001) Adv. Appl. Clifford Algebras, 11 (S3), pp. 49-68Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Multivector functions of real variable (2001) Adv. Appl. Clifford Algebras, 11 (S3), pp. 69-77Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Multivector functions of mutivector variable (2001) Adv. Appl. Clifford Algebras, 11 (S3), pp. 79-91Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Multivector functionals (2001) Adv. Appl. Clifford Algebras, 11 (S3), pp. 93-103Oliveira Capelas, E., Rodrigues Jr., W.A., Dotted and Undotted algebraic spinor fields in general relativity (2004) Int. J. Mod. Phys., D13, pp. 1637-1659Palais, R.S., (1981) The Geometrization of Physics, , in Lecture Notes from a Course at the National Tsing Hua University, Hsinchu, Taiwan, The Geometrization of PhysicsRamond, P., (1989) Field Theory: A Modern Primer, , 2nd edn. (Addison-Wesley Publ. Co., Reading, MA)Rodrigues Jr., W.A., Souza, Q.A.G., The Clifford bundle and the nature of the gravitational fields (1995) Found. Phys., 23, pp. 1465-1490Rodrigues Jr., W.A., Sharif, M., Equivalence principle and the principle of local Lorentz invariance (2002) Found. Phys., 32, pp. 811-812. , Found. Phys. 31 (2001) 1785-1806, corrigenda:Rodrigues Jr., W.A., Algebraic and Dirac-Hestenes spinor and spinor fields (2004) J. Math. Phys., 45, pp. 2908-2945Rodrigues Jr., W.A., Souza, Q.A.G., An ambiguous statement called "tetrad postulate" sand the correct field equations satisfied by the tetrad fields math-ph/0411085Sachs, R.K., Wu, H., (1977) Relativity for Mathematicians, , (Springer-Verlag, Berlin)Souza, Q.A.G., Rodrigues Jr., W.A., The Dirac operator the structure of Riemann-Cartan-Weyl Spaces (1994) Gravitation: The Spacetime Structure. Proc. SILARG VIII, pp. 179-212. , in eds. P. Letelier W. A. Rodrigues, Jr. (World Scientific Singapore)Thirring, W., Wallner, R.P., The use of exterior forms in Einstein's gravitational theory (1978) Braz. J. Phys., 8, pp. 686-723Wallner, R.P., Notes on the gauge theory and gravitation (1982) Acta Phys. Austriaca, 54, pp. 165-18
Lagrangian Formalism For Multiform Fields On Minkowski Spacetime
No full textWe present the Lagrangian formalism for multiform fields on Minkowski spacetime based on the multiform and extensor calculus. The formulation gives a unified mathematical description for the relativistic field theories including the gravitational field. We work out examples including the Dirac-Hestenes field on the gravitational background. © 2001 Plenum Publishing Corporation.401299313De Leo, S., Oziewicz, Z., Rodrigues Jr., W.A., Vaz Jr., J., The Dirac-Hestenes Lagrangian (1999) International Journal of Theoretical Physics, 38, pp. 2347-2367Moya, A.M., (1999) Lagrangian Formalism for Multivector Fields on Minkowski Spacetime, , Ph.D. Thesis, IMECC-UNICAMPMoya, A.M., Fernández, V.V., Rodrigues Jr., W.A., (2000) Clifford Multivector Fields and Extensor Fields, , in preparationManuel, M.A., Fernández, V.V., Rodrigues Jr., W.A., (2000) Gravitational Fields as Distortion Fields on Minkowski SpacetimeHestenes, D., (1966) Space-time Algebra, , Gordon and Breach, New YorkHestenes, D., Sobczyk, G., (1984) Clifford Algebra to Geometrical Calculus, , Reidel, DordrechtFernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Covariant derivatives on Minkowski manifolds (2000) Clifford Algebra and Their Applications in Mathematical Physics, Volume 1, Algebra and Physics, 1. , R. Ablamowicz and B. Fauser, Editors, Birkhauser, BostonFernández, V.V., Moya, A.M., Rodrigues Jr., W.A., (2000) The Algebraic Theory of Connections, Differential and Lie Operators for Clifford and Extensor FieldsLasenby, A., Doran, C., Gull, S., A multivector derivative approach to Lagrangian field theory (1993) Foundations of Physics, 23, pp. 1329-1356Lasenby, A., Doran, C., Gull, S., Gravity, gauge theories and geometric algebra (1998) Philosophical Transactions of the Royal Society, 356, pp. 487-582Lounesto, P., (1997) Clifford Algebras and Spinors, , Cambridge University Press, CambridgeRodrigues Jr., W.A., De Rosa, M.A.F., The meaning of time in relativity and Einstein's later view of the twin paradox (1989) Foundations of Physics, 19, pp. 705-724Rodrigues Jr., W.A., De Souza, Q.A.G., The Cifford bundle and the nature of the gravitational field (1993) Foundations of Physics, 23, pp. 1456-1490Rodrigues Jr., W.A., De Souza, Q.A.G., Vaz Jr., J., Lagrangian formulation in the Clifford bundle of the Dirac-Hestenes equation on a Riemann-Cartan manifold (1994) Gravitation: The Spacetime Structure, pp. 522-531. , Patricio Letelier and Waldyr Alves Rodrigues Jr., Editors, World Scientific, SingaporeRodrigues Jr., W.A., De Souza, Q.A.G., Vaz Jr., J., Lounesto, P., Dirac-Hestenes spinor fields on Riemann-Cartan manifolds (1995) International Journal of Theoretical Physics, 35, pp. 1849-1900Sachs, R.K., Wu, H.-H., (1977) General Relativity for Mathematicians, , Springer-Verlag, New Yor
Lagrangian Formalism In Minkowski Spacetime
No full text[No abstract available]722269292Jauch, J.M., Rorlich, F., (1976) The Theory of Photons and Electrons, , Springer-Verlag, BerlinMoya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Lagrangian Formalism for Multiform Fields on Minkowski Spacetime (2001) Int. J. Theor. Phys, 40, pp. 299-314Thirring, W., (1980) Classical Field Theory, 2. , Springer-Verlag, New Yor
Locally Inertial Reference Frames In Lorentzian And Riemann-cartan Spacetimes
No full textIn this paper the concept of locally inertial reference frames (LIRFs) in Lorentzian and Riemann-Cartan spacetime structures is scrutinized. A rigorous mathematical definition of a LIRF in both structures is given, something that needs preliminary a clear mathematical distinction between the concepts of observers, reference frames, naturally adapted coordinate functions to a given reference frame and which properties may characterize an inertial reference frame (if any) in the Lorentzian and Riemann-Cartan structures. Hopefully, the paper clarifies some obscure issues associated to the concept of a LIRF appearing in the literature, in particular the relationship between LIRFs in Lorentzian and Riemann-Cartan spacetimes and Einstein's most happy thought, i.e., the equivalence principle. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.5245302310Aldrovandi, R., Barros, P.B., Pereira, J.G., (2002) Found. Phys, 33, pp. 545-575. , [arXiv:gr-qc/0212034v1]Bishop, R.L., Goldberg, S.I., (1980) Tensor Analysis on Manifolds, , (Dover, New York)Choquet-Bruhat, Y., Dewitt-Morette, C., Dillard-Bleick, M., (1982) Analysis, Manifolds and Physics, , revised edition (North-Holland, Amsterdam)L. Fabbri, [arXiv:gr-qc/060809v3]L. Fabbri, [arXiv:09052541v3[gr-qc]]Fernández, V.V., Rodrigues Jr., W.A., (2010) Gravitation As A Plastic Distortion of the Lorentz Vacuum, Fundamental Theories of Physics, 168. , (Springer, Heidelberg)Hartley, D., (1995) Class. Quantum Gravity, 12. , L103-L105Ilieve, B.Z., (1996) J. Phys. A: Math. Gen., 29, pp. 6895-6901Ilieve, B.Z., (1997) J. Phys. A: Math. Gen., 30, pp. 4327-4336Ilieve, B.Z., (1998) J. Phys. A: Math. Gen., 31, pp. 1287-1296Ilieve, B.Z., (1998) J. Geom. Phys., 24, pp. 209-222Y. Lam, [arXiv:gr-qc/02110009v1]J.F.T. Giglio, and, W.A. Rodrigues Jr.,[arXiv:1109.5403v1[physics.gen-ph] ]Nester, J.M., (2010) Ann. Phys. (Berlin), 19, pp. 45-52Rodrigues Jr., W.A., Rosa, M.A.F., (1989) Found. Phys., 19, pp. 705-724Rodrigues Jr., W.A., Souza, Q.A.G., Bozhkov, Y., (1995) Found. Phys, 25, pp. 871-924Rodrigues Jr., W.A., Sharif, M., (2001) Found. Phys., 31, pp. 1785-1806. , corrigenda: Found. Phys 32, 811-812 (2002)Rodrigues Jr., W.A., De Oliveira, E.C., The Many Faces of Maxwell, Dirac and Einstein Equations. A Clifford Bundle Approach (2007) Lecture Notes in Physics, 722. , http://www.ime.unicamp.br/~walrod/errata14062011.pdf, (Springer, Heidelberg,)Rodrigues Jr., W.A., Rept. Math. Phys., , [arXiv:1109.5272v2 [math-ph]]Ohanian, H.C., Ruffini, R., (1994) Gravitation and Spacetime, , 2nd edition (W. W. Norton & Co., New York)M. Socolovsky, [arXiv:1009.3979[gr-qc]]Sachs, R.K., Wu, H., (1997) General Relativity for Mathematicians, , (Springer-Verlag, New York)E.L. Schücking, [arXiv:0903.3768v2[physics.hist-ph]]Von Der Heyde, P., (1975) Nuovo Cimento Lett., 14, pp. 250-25
Algebraic And Dirac-hestenes Spinors And Spinor Fields
Full text linkAlmost all presentations of Dirac theory in first or second quantization in physics (and mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of nonhomogeneous even multivectors fields) is used. However, a careful analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski space-time as some equivalence classes of pairs (ξu, ψu), where ξu is a spinorial frame field and ψu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a careful analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the bilinear covariants (on Minkowski space-time) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary Riemann-Cartan space-times. The present paper contains also Appendixes A-E which exhibits a truly useful collection of results concerning the theory of Clifford algebras (including many tricks of the trade) necessary for the intelligibility of the text. © 2004 American Institute of Physics.45729082944Ablamowicz, R., Fauser, B., (2000) Clifford Algebras and Their Applications in Mathematical Physics, Vol. 1Algebra and Physics, 1. , Birkhauser, BostonAblamowicz, R., Clifford algebras (2004) Progress in Mathematical Physics, 34. , Birkhauser, BostonAblamowicz, R., Sobczyk, G., (2004) Lectures on Clifford (Geometric) Algebras and Applications, , Birkhauser, BostonAdler, S.L., (1995) Quaternionic Quantum Mechanics and Quantum Fields, , Oxford University Press, OxfordAharonov, Y., Susskind, L., Observality of the sign of spinors under a 2π rotation (1967) Phys. Rev., 158, pp. 1237-1238Atyah, M.F., Bott, R., Shapiro, A., Clifford modules (1964) Topology, 3, pp. 3-38Ashdown, M.A.J., Somarro, S.S., Gull, S.F., Doran, C.J.L., Multilinear representations of rotation groups within geometric algebra (1998) J. Math. Phys., 39, pp. 1566-1588Barut, A.O., Bracken, X., Zitterbewegung and the internal geometry of the electron (1981) Phys. Rev. D, 23, pp. 2454-2463Barut, A.O., Zanghi, N., Classical model of the Dirac electron (1984) Phys. Rev. Lett., 52, pp. 2009-2012Barut, A.O., Excited states of Zitterbewegung (1990) Phys. Lett. B, 237, pp. 436-439Baylis, W.E., (1996) Clifford (Geometric) Algebras with Applications in Physics, Mathematics and Engineering, , Birkhäuser, BostonBaylis, W., (1999) Electrodynamics, A Modern Geometric Approach, , Birkhauser, BostonBjorken, J.D., Drell, S., (1964) Relativistic Quantum Mechanics, , McGraw-Hill, New YorkBeen, I.M., Tucker, R.W., An Introduction to Spinors and Geometries with Applications in Physics, , Hilger, BristolBeen, I.M., Tucker, R.W., Representing spinors with differential forms, in (1988) Spinors in Physics and Geometry, , edited by A. Trautman and G. Furlan (World Scientific, Singapore)Berezin, F.A., (1996) The Method of Second Quantization, , Academic, New YorkBerezin, F.A., Marinov, M.S., Particle spin dynamics as the Grassmann variant of classical mechanics (1997) Ann. Phys. (N.Y.), 104, pp. 336-362Bayro-Corrochano, E., Zhang, Y.A., The motor extended Kalman filter: A geometrical approach for 3D rigid motion estimation (2000) J. Math. Imaging Vision, 13, pp. 205-227Bayro-Corrochano, E., (2001) Geometrical Computing for Perception Action Systems, , Springer, BerlinBlaine Lawson Jr., H., Michelshon, M.L., (1989) Spin Geometry, , Princeton University Press, Princeton, NJBleecker, D., (1981) Gauge Theory and Variational Principles, , Addison-Wesley Reading, MABrauer, R., Weyl, H., Spinors in n dimensions (1935) Am. J. Math., 57, pp. 425-449Budinich, P., Trautman, A., (1998) The Spinorial Chessboard, , Springer, BerlinCartan, E., (1996) The Theory of Spinors, , MIT Press, Cambridge, MACastro, C., Hints of a new relativity principle from p-brane quantum mechanics (2000) Chaos, Solitons Fractals, 11, pp. 1721-1737Castro, C., The status and programs of the new relativity theory (2001) Chaos, Solitons Fractals, 12, pp. 1585-1606Castro, C., The string uncertainty relations follow from the new relativity principle (2000) Found. Phys., 30, pp. 1301-1316Castro, C., Is quantum spacetime infinite dimensional (2000) Chaos, Solitons Fractals, 11, pp. 1663-1670Castro, C., Noncommutative Quantum Mechanics and Geometry from Quantization in C-spaces, , hep-th/0206181Castro, C., A derivation of the black-hole area-entropy relation in any dimension (2001) Entropie, 3, pp. 12-26Castro, C., Granik, A., Extended scale relativity, p-loop harmonic oscillator and logarithmic corrections to the black hole entropy (2003) Found. Phys., 33, pp. 445-466Castro, C., Pavsic, M., Higher derivative gravity and torsion from the geometry of C-spaces (2002) Phys. Lett. B, 539, pp. 133-142Castro, C., Generalized p-forms electrodynamics in Clifford space (2004) Mod. Phys. Lett. A, 19, pp. 19-29Castro, C., Pavsic, M., The extended relativity theory in Clifford spaces Int. J. Mod. Phys., , to be publishedChallinor, A., Lasenby, A., Doran, C., Gull, S., Massive, non-ghost solutions for the Dirac field coupled self-consistently to gravity (1997) Gen. Relativ. Gravit., 29, pp. 1527-1544Challinor, A., Lasenby, A., Somaroo, C., Doran, C., Gull, S., Tunnelling times of electrons (1997) Phys. Lett. A, 227, pp. 143-152Challinor, A., Lasenby, A., Doran, C., A relativistic, causal account of spin measurement (1996) Phys. Lett. A, 218, pp. 128-138Chevalley, C., (1954) The Algebraic Theory of Spinors, , Columbia University Press, New YorkChevalley, C., (1997) The Algebraic Theory of Spinors and Clifford Algebras. Collect Works Vol. 2, 2. , Springer-Verlag, BerlinChoquet-Bruhat, Y., (1968) Géométrie Différentielle et Systèmes Extérieurs, , Dunod, ParisChoquet-Bruhat, Y., Dewitt-Morette, C., Dillard-Bleick, M., (1982) Analysis, Manifolds and Physics, Revised Edition, , North-Holland, AmsterdamColombo, F., Sabadini, I., Sommen, F., Struppa, D.C., Computational Algebraic Analysis (2004) Progress in Mathematical Physics, , Birkhauser, BostonCrawford, J., On the algebra of Dirac bispinor densities: Factorization and inversion theorems (1985) J. Math. Phys., 26, pp. 1439-2144Crummeyrolle, A., (1991) Orthogonal and Sympletic Clifford Algebras, , Kluwer Academic, DordrechtDaviau, C., (1993) Equation de Dirac non Linéaire, , Thèse de doctorat, Univ. de NantesDaviau, C., Solutions of the Dirac equation and a non linear Dirac equation for the hydrogen atom (1997) Adv. Appl. Clifford Algebras, 7, pp. 175-194Delanghe, R., Sommen, F., Souček, V., Clifford algebra and spinor-valued functions: A function theory for the dirac operator (1992) Mathematics and Its Applications, 53. , Kluwer Academic, DordrechtDe Leo, S., Rodrigues Jr., W.A., Quantum mechanics: From complex to complexified quaternions (1997) Int. J. Theor. Phys., 36, pp. 2725-2757De Leo, S., Rodrigues Jr., W.A., Quaternionic electron theory: Dirac's equation (1998) Int. J. Theor. Phys., 37, pp. 1511-1529De Leo, S., Rodrigues Jr., W.A., Quaternionic electron theory: Geometry, algebra and Dirac's spinors (1998) Int. J. Theor. Phys., 37, pp. 1707-1720De Leo, S., Rodrigues Jr., W.A., Vaz Jr., J., Complex geometry and Dirac equation (1998) Int. J. Theor. Phys., 37, pp. 2415-2431De Leo, S., Rodrigues Jr., W.A., Vaz Jr., J., Dirac-hestenes lagrangian (1999) Int. J. Theor. Phys., 38, pp. 2349-2369Dirac, P.A.M., The quantum theory of the electron (1928) Proc. R. Soc. London, Ser. A, 117, pp. 610-624Doran, C.J.L., Lasenby, A., Challinor, A., Gull, S., Effects of spin-torsion in gauge theory gravity (1998) J. Math. Phys., 39, pp. 3303-3321Doran, C.J.L., Lasenby, A., Gull, S., The physics of rotating cylindrical strings (1996) Phys. Rev. D, 54, pp. 6021-6031Doran, C.J.L., Lasenby, A., Somaroo, S., Challinor, A., Spacetime algebra and electron physics (1996) Adv. Imaging Electron Phys., 95, pp. 271-386Doran, C.J.L., New form of the Kerr solution (2000) Phys. Rev. D, 61, p. 067503Doran, C., Lasenby, A., (2003) Geometric Algebra for Physicists, , Cambridge University Press, CambridgeDorst, L., Doran, C., Lasenby, J., (2002) Applications of Geometric Algebra in Computer Science and Engineering, , Birkhauser, BostonFauser, B., A Treatise on Quantum Clifford Algebras, , math.QA/022059Felzenwalb, B., (1979) Álgebras de Dimensão Finita, , Instituto de Matemática Pura e Aplicada (IMPA), Rio de JaneiroFernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Covariant derivatives on minkowski manifolds (2000) Clifford Algebras and Their Applications in Mathematical Physics, Vol. 1: Algebra and Physics, 1. , edited by R. Ablamowicz and B. Fauser (Birkhauser, Boston)Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Euclidean clifford algebra space (2001) Adv. Appl. Clifford Algebras, 11, pp. 1-21Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Extensors (2001) Adv. Appl. Clifford Algebras, 11, pp. 23-43Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Metric tensor vs metric extensor (2001) Adv. Appl. Clifford Algebras, 11, pp. 43-51Fierz, M., Zur FermischenTheorie des β-zerfals (1937) Z. Phys., 104, pp. 553-565Figueiredo, V.L., Rodrigues Jr., W.A., Oliveira, E.C., Covariant, algebraic and operator spinors (1990) Int. J. Theor. Phys., 29, pp. 371-395Figueiredo, V.L., Rodrigues Jr., W.A., Oliveira, E.C., Clifford algebras and the hidden geometrical nature of spinors (1990) Algebras, Groups Geom., 7, pp. 153-198Frankel, T., (1997) The Geometry of Physics, , Cambridge University Press, CambridgeFuruta, S., Doran, C.J.L., Havel, S.-G., Measurement with SAW-guided electrons (2002) Proceedings, Sixth International Conference on Clifford Algebras and Their Applications, , TennesseeGsponer, A., On the 'equivalence' of maxwell and dirac equations (2002) Int. J. Theor. Phys., 41, pp. 689-694Geroch, R., Spinor structure of spacetimes in general relativity. I (1968) J. Math. Phys., 9, pp. 1739-1744Graf, W., Differential forms as spinors (1978) Ann. Inst. Henri Poincare, Sect. A, 29, pp. 85-109Gull, S.F., Lasenby, A.N., Doran, C.J.L., Electron paths tunnelling and diffraction in the spacetime algebra (1993) Found. Phys., 23, pp. 1329-1356Gurtler, R., Hestenes, D., Consistency in the formulation of Dirac, Pauli and Schrodinger theories (1975) J. Math. Phys., 16, pp. 573-583Harvey, F.R., (1990) Spinors and Calibrations, , Academic, San DiegoHavel, T.F., Doran, C.J.L., Furuta, S., Density operators in the multiparticle spacetime algebra Proc. R. Soc., , to be publishedHermann, R., Spinors, Clifford and Caley algebras (1974) Interdisciplinariy Mathematics, 7. , Rutgers University, New Brunswick, NJHestenes, D (1966) Space-time Algebra, , Gordon and Breach, New York, 1987Hestenes, D., Real spinor fields (1967) J. Math. Phys., 8, pp. 798-808Hestenes, D., Observables, operators, and complex numbers in Dirac theory (1975) J. Math. Phys., 16, pp. 556-571Hestenes, D., Local observables in Dirac theory (1973) J. Math. Phys., 14, pp. 893-905Hestenes, D., Proper particle mechanics (1974) J. Math. Phys., 15, pp. 1768-1777Hestenes, D., Proper dynamics of a rigid point particle (1974) J. Math. Phys., 15, pp. 1778-1786Hestenes, D., Observables operators and complex numbers in the Dirac theory (1975) J. Math. Phys., 16, pp. 556-572Hestenes, D., Sobczyk, G., (1984) Clifford Algebra to Geometrical Calculus, , Reidel, DordrechtHestenes, D., Space-time structure of weak and electromagnetic interactions (1982) Found. Phys., 12, pp. 153-168Hestenes, D., Quantum mechanics from self-interaction (1985) Found. Phys., 15, pp. 63-87Hestenes, D., The Zitterbewegung interpretation of quantum mechanics (1990) Found. Phys., 20, pp. 1213-1232Hestenes, D., A spinor approach to gravitational motion and precession (1986) Int. J. Theor. Phys., 25, pp. 1013-1028Hestenes, D., Invariant body kinematics I: Saccadic and compensatory eye movements (1993) Neural Networks, 7, pp. 65-77Hestenes, D., Invariant body kinematics II: Reaching and neurogeometry (1993) Neural Networks, 7, pp. 79-88Hladik, J., (1999) Spinors in Physics, , Springer-Verlag, BerlinHurley, D.J., Vandyck, M.A., (1999) Geometry, Spinors and Applications, , Springer-Verlag, BerlinIvanenko, D., Obukov, N.Yu., Gravitational interaction of fermion antisymmetric connection in general relativitiy (1985) Ann. Phys. (N.Y.), 17, pp. 59-70Jancewicz, B., (1989) Multivectors and Clifford Algebra in Electrodynamics, , World Scientific, SingaporeKähler, E., Der innere differentialkalkül (1962) Rediconti Matematica Appl, 21, pp. 425-523Knus, M.A., Quadratic forms (1988) Clifford Algebras and Spinors, , Univ. Estadual de Campinas (UNICAMP), CampinasLasenby, J., Bayro-Corrochano, E.J., Lasenby, A., Sommer, G., A new methodology for computing invariants in computer vison (1996) IEEE Proc. of the International Conf. on Pattern Recognition, ICPR' 96, 1, pp. 93-397. , Viena, AustriaLasenby, J., Bayro-Corrochano, E.J., Computing 3D projective invariants from points and lines (1997) 7th Int. Conf., CAIP' 97, pp. 82-89. , Computer Analysis of Images and Patterns, edited by G. Sommer, K. Daniilisis, and X. Pauli, Kiel (Springer-Verlag, Berlin)Lasenby, J., Bayro-Corrochano, E.J., Analysis and computation of projective invariants from multiple views in the geometrical algebra framework (1999) Int. J. Pattern Recognit. Artif. Intell., 13, pp. 1105-1121Lasenby, A., Doran, C., Grassmann calculus, pseudoclassical mechanics and geometric algebra (1993) J. Math. Phys., 34, pp. 3683-3712Lasenby, A., Doran, C., Gull, S., Gravity, gauge theories and geometric algebra (1998) Philos. Trans. R. Soc. London, Ser. A, 356, pp. 487-582Lasenby, J., Lasenby, A.N., Doran, C.J.L., A unified mathematical language for physics and engineering in the 21st century (2000) Philos. Trans. R. Soc. London, Ser. A, 358, pp. 21-39Lasenby, A., Doran, C.J.L., Geometric algebra, Dirac wavefunctions and black holes (2002) Advances in the Interplay between Quantum and Gravity Physics, pp. 251-283. , edited by P. G. Borgmann and V. de Sabbata (Kluwer Academic, Dordrecht)Lichnerowicz, A., Champs spinoriales et propagateurs en relativité générale (1964) Ann. Inst. Henri Poincare, Sect. A, 13, pp. 233-320Lewis, A., Doran, C., Lasenby, A., Electron scattering without spin sums (2001) Int. J. Theor. Phys., 40, pp. 363-375Lichnerowicz, A., Champ de Dirac, Champ du neutrino et transformations C, P, T sur un espace temps courbe (1984) Bull. Soc. Math. France, 92, pp. 11-100Lounesto, P., (2001) Clifford Algebras and Spinors, 2nd Ed., , Cambridge University Press, CambridgeMarchuck, N., A Concept of Dirac-type Tensor Equations, , math-ph/0212006Marchuck, N., Dirac-type tensor equations with non Abelian gauge symmetries on pseudo-Riemannian space (2002) Nuovo Cimento Soc. Ital. Fis., B, 117 B, pp. 613-614Marchuck, N., The Dirac equation vs. the Dirac type tensor equation (2002) Nuovo Cimento Soc. Ital. Fis., B, 117 B, pp. 511-520Marchuck, N., Dirac-type Equations on A Parallelisable Manifolds, , math-ph/0211072Marchuck, N., Dirac-type tensor equations with non-Abelian gauge symmetries on pseudo-Riemannian space (2002) Nuovo Cimento Soc. Ital. Fis., B, 117 B, pp. 95-120Marchuck, N., The Tensor Dirac Equation in Riemannian Space, , math-ph/0010045Marchuck, N., A Tensor Form of the Dirac Equation, , math-ph/0007025Marchuck, N., A gauge model with spinor group for a description of a local interaction of a Fermion with electromagnetic and gravitational fields (2000) Nuovo Cimento Soc. Ital. Fis., B, 115 B, pp. 11-25Marchuck, N., Dirac Gamma-equation, Classical Gauge Fields and Clifford Algebra, , math-ph/9811022Matteuci, P., (2003) Gravity, Spinors and Gauge Natural Bundles,", , http://www.maths.soton.ac.uk/~pnm/phdthesis.pdf, Ph.D. thesis, Univ. SouthamptonMiller Jr., W., (1972) Symmetry Groups and Their Applications, , Academic, New YorkMiralles, D.E., (2001) Noves Applications de l'Algebra Geomètrica a la Física Matemàtica, , Ph.D. thesis, Department de Física Fonamental, Universitat de BarcelonaMisner, C.W., Wheeler, J.A., Classical physics as geometry-gravitation, electromagnetism, unquantized charge, and mass as properties of curved empty space (1957) Ann. Phys. (N.Y.), 2, pp. 525-603Mosna, R.A., Miralles, D., Vaz Jr., J., Multivector Dirac equations and Z2-gradings Clifford algebras (2002) Int. J. Theor. Phys., 41, pp. 1651-1671Mosna, R.A., Miralles, D., Vaz Jr., J., Z2-gradings on Clifford algebras and multivector structures (2003) J. Phys. A, 36, pp. 4395-4405Mosna, R.A., Vaz Jr., J., Quantum tomography for Dirac spinors (2003) Phys. Lett. A, 315, pp. 418-425Mosna, R.A., Rodrigues Jr., W.A., The bundles of algebraic and Dirac-Hestenes spinor fields J. Math. Phys., , in pressMoya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Metric Clifford algebra (2001) Adv. Appl. Clifford Algebras, 11, pp. 53-73Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Multivector functions of a real variable (2001) Adv. Appl. Clifford Algebras, 11, pp. 75-83Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Multivector functions of mutivector variable (2001) Adv. Appl. Clifford Algebras, 11, pp. 85-98Moya, A.M., Fernández, V.V., Rodrigues Jr., W.A., Multivector functional (2001) Adv. Appl. Clifford Algebras, 11, pp. 99-109Naber, G.L., Topology (2000) Appl. Math. Sci., 141. , Geometry and Gauge Fields. Interactions, (Springer-Verlag, New York)Nakahara, M., Geometry (1990) Topology and Physics, , Institute of Physics, BristolNicolescu, L.I., Notes on Seiberg-Witten Theory (2000) Graduate Studies in Mathematics, 28. , AMS, Providence, RIOliveira, E.C., Rodrigues Jr., W.A., Clifford Valued Differential Forms, Algebraic Spinor Fields, Gravitation, Electromagnetism and "Unified" Theories,", , math-ph/0311001Pavšic, M., Recami, E., Rodrigues Jr., W.A., Macarrone, G.D., Racciti, F., Salesi, G., Spin and electron structure (1993) Phys. Lett. B, 318, pp. 481-488Pav̌sic, M., The landscape of theoretical physics: A global view-from point particles to the brane world and beyond in search of a unifying principle (2001) Fundamental Theories of Physics, 119. , Kluwer Academic, DordrechtPav̌sic, M., Clifford algebra based polydimensional relativity and relativistic dynamics (2001) Found. Phys., 31, pp. 1185-1209Pav̌sic, M., How the geometric calculus resolves the ordering ambiguity of quantum theory in curved space (2003) Class. Quantum Grav., 20, pp. 2697-2714Penrose, R., Rindler, W (1986) Spinors and Spacetitne, 1. , Cambridge University Press, CambridgePezzaglia Jr., W.M., Dimensionality democratic calculus and principles of polydimensional physics (2000) Clifford Algebras and Their Applications in Mathematical Physics, Vol 1: Algebras and Physics, 1. , edited by R. Ablamowicz and B. Fauser Birkhauser, BostonPorteous, I.R., (1981) Topological Geometry, 2nd Ed., , Cambridge University Press, CambridgePorteous, I.R., (2001) Clifford Algebras and the Classical Groups, 2nd Ed., , Cambridge University Press, CambridgeRainich, G.Y., Electromagnetism in general relativity (1925) Trans. Am. Math. Soc., 27, pp. 106-136Raševskil, P.K., The theory of spinors (1955) Usp. Mat. Nauk, 10, pp. 3-110Ryan, J., Sproessig, W., (2000) Clifford Algebras and Their Applications in Mathematical Physics, Vol 2: Clifford Analysis, 2. , Birkhauser, BostonRiesz, M., Clifford numbers and spinors (1993) Lecture Series, 28. , The Institute for Fluid Mechanics and Applied Mathematics, Univ. Maryland, 1958. Reprinted as facsimile, E. F. Bolinder, and P. Lounesto (eds.) (Kluwer Academic, Dordrecht)Riesz, M., L' equation de Dirac en relativité générale (1954) Skandinaviska Matematikerkongressen I Lund 1953, pp. 241-259. , Håkan Ohlssons Boktryckeri, Lund(1988) Marcel Riez, Collected Papers, pp. 814-832. , L. Gårdening and L. Hömander (eds.), (Springer, New York)Rodrigues Jr., W.A., Oliveira, E.C., Dirac and Maxwell equations in the Clifford and spin-Clifford bundles (1990) Int. J. Theor. Phys., 29, pp. 397-411Rodrigues Jr., W.A., Vaz Jr., J., About Zitterbewegung and electron structure (1993) Phys. Lett. B, 318, pp. 623-628Rodrigues Jr., W.A., Souza, Q.A.G., Vaz Jr., J., Lounesto, P., Dirac-Hestenes spinor fields on Riemann-Cartan manifolds (1995) Int. J. Theor. Phys., 35, pp. 1854-1900Rodrigues Jr., W.A., Souza, Q.A.G., Vaz, J., Spinor fields and superfields as equivalence classes of exterior algebra fields (1995) Clifford Algebras and Spinor Structures, pp. 177-198. , edited by R. Abramovicz and P. Lounesto (Kluwer Academic Dordrecht)Rodrigues Jr., W.A., Vaz Jr., J., Pavšic, M., The Clifford bundle and the dynamics of the superparticle (1996) Banach Cent Publ., 37, pp. 295-314Rodrigues Jr., W.A., Vaz Jr., J., From electromagnetism to relativistic quantum mechanics (1998) Found. Phys., 28, pp. 789-814Rodrigues Jr., W.A., Souza, Q.A.G., The Clifford bundle and the nature of the gravitational field (1993) Found. Phys., 23, pp. 1465-1490Rodrigues Jr., W.A., Maxwell-Dirac equivalences of the first and second kinds and the Seiberg-Witten equations (2003) Int. J. Math. Math. Sci
The Effective Lorentzian And Teleparallel Spacetimes Generated By A Free Electromagnetic Field
No full textIn this paper we show that a free electromagnetic field living in Minkowski spacetime generates an effective Weitzenböck or an effective Lorentzian spacetime whose properties are determined in details. These results are possible because using the Clifford bundle formalism we found a noticeable result that the energy-momentum densities of a free electromagnetic field are sources of the Hodge duals of exact 2-form fields which satisfy Maxwell like equations. © 2008 Polish Scientific Publishers PWN, Warszawa.6216989Hestenes, D., (1966) Space Time Algebra, , Gordon and Breach, New YorkFernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Extensors (2001) Adv. Appl. Clifford Algebras, 11, p. 23Notte-Cuello, E., Rodrigues Jr., W.A., A Maxwell Like Formulation of Gravitational Theory in Minkowski Spacetime (2007) Int. J. Mod. Phys. D, 16, p. 1027Notte-Cuello, E., Rodrigues Jr., W.A., Superposition principle and the problem of the additivity of energies and momenta of distinct electromagnetic fields (2008) Rep. Math. Phys., 62, pp. 91-101Misner, C.W., Wheeler, J.A., Classical Physics and Geometry: Gravitation, Electromagnetism, Unquantized Charge and Mass as Properties of Curved Empty Spacetime (1957) Ann. Phys., 2, p. 525Mosna, R.A., Rodrigues Jr., W.A., The bundles of algebraic and Dirac-Hestenes spinor fields (2004) J. Math. Phys., 45, p. 2954Rainich, G.Y., Electrodynamics in the General Relativity Theory (1925) Trans. Am. Math. Soc., 27, p. 106Riesz, M., Clifford Numbers and Spinors: with Riesz's Private Lectures to E. Folke Bolinder and a Historical Review by Pertti Lounesto (1993) Fundamental Theories of Physics, 54. , Springer, BerlinRodrigues Jr., W.A., de Souza, Q.A.G., da Rocha, R., Conservation Laws on Riemann-Cartan, Lorentzian and Teleparallel Spacetimes I. Conservation Laws (2007) Bulletin Soc. des Sci. et Lettres de Lódz 57, Ser. Recherches sur les Deformations, 52, pp. 37-65Rodrigues Jr., W.A., de Souza, Q.A.G., da Rocha, R., Conservation Laws on Riemann-Cartan,Lorentzian and Teleparallel Spacetimes II. Appendix on Clifford Bundles, Maxwell Theory and Teleparallel Spacetimes (2007) Bulletin Soc. des Sci. et Lettres de Lódz 57, Ser. Recherches sur les Deformations, 52, pp. 67-77Rodrigues Jr., W.A., Capelas de Oliveira, E., The Many Faces of Maxwell, Dirac and Einstein Equations. A Clifford Bundle Approach (2007) Lecture Notes in Physics, 722. , Springer, HeidelbergThirring, W., (1980) Classical Field Theory, 2. , Springer, New YorkThirring, W., Wallner, R., The use of exterior forms in Einstein's gravitational theory (1978) Brazilian J. Phys., 8, p. 86
The Hidden Geometrical Nature Of Spinors
No full text[No abstract available]7226194Aharonov, Y., Susskind, L., Observability of the Sign of Spinors under a 2π Rotation (1967) Phys. Rev, 158, pp. 1237-1238Ahluwalia-Khalilova, D. V., and Grumiller D., Spin Half Fermions, with Mass Dimension One: Theory, Phenomenology, and Dark Matter, JCAP 07, 012 (2005). [hep-th/0412080]Benn, I.M., Tucker, R.W., (1987) An Introduction to Spinors and Geometry with Applications in Physics, , Adam Hilger, BristolBjorken, J.D., A Dynamical Origin for the Electromagnetic Field (1963) Ann. Phys.(New York), 24, pp. 174-187Chevalley, C., (1997) The Algebraic Theory of Spinors and Clifford Algebras, , Springer-Verlag, BerlinChoquet-Bruhat, Y., DeWitt-Morette, C., Dillard-Bleick, M., (1982) Analysis, Manifolds and Physics, , revisited edition, North Holland Publ. Co, AmsterdamCrawford, J., On the Algebra of Dirac Bispinor Densities: Factorization and Inversion Theorems (1985) J. Math. Phys, 26, pp. 1439-1441Crumeyrolle, A., (1990) Orthogonal and Sympletic Clifford Algebras, , Kluwer Acad. Publ, DordrechtFigueiredo, V.L., Rodrigues Jr., W.A., Oliveira, E., Capelas de, Covariant, Algebraic and Operator Spinors (1990) Int. J. Theor. Phys, 29, pp. 371-395Figueiredo, V.L., Rodrigues Jr., W.A., Oliveira, E., Capelas de., Clifford Algebras and the Hidden Geometrical Nature of Spinors (1990) Algebras, Groups and Geometries, 7, pp. 153-198Lawson, Blaine Jr., H., Michelson, M.L., (1989) Spin Geometry, , Princeton University Press, PrincetonLounesto, P., Clifford Algebras and Hestenes Spinors (1993) Found. Phys, 23, pp. 1203-1237Lounesto, P., Clifford Algebras, Relativity and Quantum Mechanics (1994) Gravitation: The Spacetime Structure, pp. 50-81. , P. Letelier and W. A. Rodrigues Jr, eds, World Sci. Publ. Co, SingaporeLounesto, P., (1997) Clifford Algebras and Spinors, , Cambridge Univ. Press, CambridgeLounesto, P., Scalar Product of Spinors and an Extension of the Brauer-Wall Groups (1981) Found. Phys, 11, pp. 721-740Miller Jr., W., (1972) Symmetry Groups and their Applications, , Academic Press, New YorkMosna, R.A., Miralles, D., Vaz Jr., J., Multivector Dirac Equations and Z2-Gradings Clifford Algebras (2002) Int. J. Theor. Phys, 41, pp. 1651-1671Mosna, R. A., Miralles, D., and Vaz, J., Jr., Z2-Gradings on Clifford Algebras and Multivector Structures, J. Phys. A: Math. Gen. 36 4395-4405 (2003). [math-ph/0212020]Porteous, I.R., (1981) Topological Geometry, , second edition, Cambridge Univ. Press, CambridgePorteous, I.R., (2001) Clifford Algebras and the Classical Groups, , second edition, Cambridge Univ. Press, CambridgeRodrigues, W. A. Jr., Algebraic and Dirac-Hestenes Spinors and Spinor Fields, J. Math. Physics 45, 2908-2944 (2004). [math-ph/ 0212030]da Rocha, R., and Rodrigues, W.A. Jr., Where are ELKO Spinor Field in Lounesto Spinor Field Classification?, Mod. Phys. Lett. A, 21 65-76 (2006). [math-phys/0506075]Zeni, J.R.R., Rodrigues Jr., W.A., A Thoughtful Study of Lorentz Transformations by Clifford Algebras (1992) Int. J. Mod. Phys. A, 7, pp. 1793-181
Gravitational Theory In Minkowski Spacetime
No full text[No abstract available]722327342Abrams, L. S., Alternative Space-Time for the Point Mass, Phys. Rev. D 20, 2474-2479 (1979). [gr-qc/0201044]de Andrade, V.C., Guillen, L.C.T., Pereira, J.G., Gravitational Energy-Momentum Density in Teleparallel Gravity (2000) Phys. Rev. Lett, 84, pp. 4533-4536Chapline, G., Dark Energy Stars (2004) Proc. of the Texas Conference on Relativistic Astrophysics, , Stanford, CA, Dec, astro-ph/0503200Cooperstock, F.I., Tieu, S., Closed Timelike Curves Re-examined, , gr/qc/0495114Davies, P., (2001) How to Build Time Machines, , Allen Lane, The Penguin Press, LondonDoran, C., Lasenby, A., (2003) Geometric Algebra for Physicists, , Cambridge University Press, CambridgeFernández, V. V., Moya, A. M. and Rodrigues, W. A. Jr., Euclidean Clifford Algebra, Adv. Appl. Clifford Algebras 11, 1-21 (2001). [math-ph/0212043]Fernández, V. V., Moya, A. M. and Rodrigues, W. A. Jr., Extensors, Adv. Appl. Clifford Algebras 11, 23-40 (2001). [math-ph/0212046]Fernández, V.V., Moya, A.M., Rodrigues Jr., W.A., Metric Tensor Vs. Metric Extensor (2001) Adv. Appl. Clifford Algebras, 11, pp. 41-48. , mathph/0212048Fernández, V. V., Moya, A. M. and Rodrigues, W. A. Jr., Metric Clifford Algebra, Adv. Appl. Clifford Algebras 11, 49-68 (2001). [math-ph/0212049]Fernández, V. V, Moya, A. M., and Rodrigues, W. A. Jr., Covariant Derivatives on Minkowski Manifolds, in R. Ablamowicz and B. Fauser (eds.), Clifford Algebras and their Applications in Mathematical Physics (Ixtapa-Zihuatanejo, Mexico 1999), 1, Algebra and Physics, Progress in Physics 18, pp 373-398, Birkhäuser, Boston, Basel and Berlin, 2000Frankel, T., (1997) The Geometry of Physics, , Cambridge University Press, CambridgeGott, J.R., (2001) Time Travel in Einstein's Universe, , Weidenfeld & Nicolson, LondonHawking, S.W., The Information Paradox for Black Holes (2004) Lecture at the 17th Int. Conf. on General Relativity and Gravitation, July, , http://www.gr17.com, DublinHayard, S.A., The Disinformation Problem for Black Holes, 14th (2004) Workshop on General Relativity and Gravitation, Kyoto University, Dec, , grqc/0504037Hayashi, K. and Shirafuji. T., New General Relativity, Phys. Rev. D 19, 3542-3553 (1979)Lasenby, A., Doran, C., Gull, S., Gravity, Gauge Theories and Geometric Algebras (1998) Phil. Trans. R. Soc, 356, pp. 487-582Logunov, A.A., Mestvirishvili, M.A., (1989) The Relativistic Theory of Gravitation, , Mir Publ, MoscowLogunov, A.A., (1999) Relativistic Theory of Gravity, , Nova Science Publ, New YorkMaluf, J.W., Hamiltonian Formulation of the Teleparallel Description of General Relativity (1994) J. Math. Phys, 35, pp. 335-343Mottola, E., Mazur, P., Gravitational Condensate Stars (2004) Proc. Nat. Acad. Sci, 111, pp. 9550-9546Moya, A. M., Fernández, V. V., and Rodrigues, W. A. Jr., Multivector Functions of a Real Variable, Adv. Appl. Clifford Algebras 11 69-77 (2001). [math.GM/0212222]Moya, A. M., Fernández, V. V., and Rodrigues, W. A. Jr., Multivector Functions of a Multivector Variable, Adv. Appl. Clifford Algebras 11, 79-91 (2001). [math.GM/0212223]Moya, A. M., Fernández, V. V., and Rodrigues, W. A. Jr., Multivector Functionals, Adv. Appl. Clifford Algebras 11, 93-103 (2001). [math.GM/0212224]Notte-Cuello, E., da Rocha, R., Rodrigues Jr., W.A., The Effective Lorentzian and Teleparallel Spacetimes Generated by a Free Electromagnetic Field, , gr-qc/0612098Notte-Cuello, E., Rodrigues Jr., W.A., A Maxwell Like Formulation of Gravitational Theory in Minkowski Spacetime, , math-ph/0608017Novikov, I.D., (1998) The River of Time, , Cambridge University Press, Cambridgeda Rocha, R., Rodrigues Jr., W.A., The Einstein-Hilbert Lagrangian Density in a 2-Dimensional Spacetime is an Exact Differential (2006) Mod. Phys. Lett. A, 21, pp. 1519-1527. , hep-th/0512168Stravroulakis, N., Scientifique, V., Noirs, T., Le Abus du Formalism (1999) Ann. Fond. L. de Broglie, 24, pp. 67-108Thirring, W., (1980) Classical Field Theory, 2. , Springer-Verlag, New Yor
Maxwell, Dirac And Seiberg-witten Equations
No full text[No abstract available]722363392Campolattaro, A.A., New Spinor Representation of Maxwell Equations 2. Generalities (1980) Int. J. Theor. Phys, 19, pp. 127-138Campolattaro, A.A., Generalized Maxwell Equations and Quantum Mechanics 1. Dirac Equation for the Free Electron (1980) Int. J. Theor. Phys, 19, pp. 141-155Campolattaro, A.A., Generalized Maxwell Equations and Quantum Mechanics 2. Generalized Dirac Equation (1980) Int. J. Theor. Phys, 19, pp. 477-482Campolattaro, A. A., From Classical Electrodynamics to Relativistic Quantum Mechanics, in J. Keller and Z. Ozwiecz (eds.), The Theory of the Electron, Adv. Appl. Clifford Algebras 7 (S), 167-173 (1997)Campolattaro, A.A., New Spinor Representation of Maxwell Equations 1. Generalities (1980) Int. J. Theor. Phys, 19, pp. 99-126Carvalho, A.L.T., Rodrigues Jr., W.A., The Non Sequitur Mathematics and Physics of the 'New Electrodynamics' Proposed by the AIAS group (2001) Random Operators and Stochastic Equations, 9, pp. 161-206Chown, M., Double or quit (2000) New Scientist, (2000), pp. 24-27. , October 14Evans, M.W., The Elementary Static Magnetic Field of the Photon (1992) Physica B, 182, pp. 227-236Evans, M.W., Vigier, J.P., The Enigmatic Photon (1994) The Field B (3), 1. , Kluwer Acad. Publ, DordrechtEvans, M.W., Vigier, J.P., The Enigmatic Photon (1995) Non Abelian Electrodynamics, 2. , Kluwer Acad. Publ, DordrechtEvans, M.W., Vigier, J.P., Roy, S., Jeffers, S., The Enigmatic Photon (1996) Theory and Practice of the B (3) Field, 3. , Kluwer Acad. Publ, DordrechtEvans, M. W., Vigier, J. P., Roy, S. and Hunter, G., The Enigmatic Photon, 4: New Directions, Kluwer Acad. Publ., Dordrecht, 1998Evans, M.W., Vigier, J.P., The Enigmatic Photon (1999) O(3) Electrodynamics, 5. , Kluwer Acad. Publ, DordrechtEvans, M.W., Crowell, L.B., (2000) Classical and Quantum Electrodynamics and the B (3) Field, , World Sci. Publ. Co, SingaporeFushchich, W.I., Nikitin, A.G., (1987) Symmetries of Maxwell Equations, , D. Reidel Publ. Co, DordrechtGsponer, A., On the, Equivalence of Maxwell and Dirac Equations (2002) Int. J. Theor. Phys, 41, pp. 689-694Gursey, F., Contribution to the Quaternion Formalism in Special Relativity (1956) Rev. Fac. Sci. Istanbul A, 20, pp. 149-171Hestenes, D., (1966) Spacetime Algebra, , Gordon and Breach Sci. Publ, New YorkJackson, J.D., (1975) Classical Electrodynamics, , second edition, John Wiley & Sons, Inc, New YorkJauch, J.M., Rorlich, F., (1976) The Theory of Photons and Electrons, , Springer-Verlag, BerlinKurşunoǧlu, B., (1962) Modern Quantum Theory, , W. H. Fremman and Co, San Francisco and LondonLandau, L.D., Lifshitz, E.M., (1975) The Classical Theory of Fields, fourth, , revised English edition, Pergamon Press, New YorkLochak, G., Wave Equation for a Magnetic Monopole (1985) Int. J. Theor. Phys, 24, pp. 1019-1050Maia Jr., A., Recami, E., Rosa, M.A.F., Rodrigues Jr., W.A., Magnetic Monopoles Without String in the Kähler-Clifford Algebra Bundle (1990) J. Math. Phys, 31, pp. 502-505Majorana, E., Teoria Relativistica di Particelle con Momento Intrinseco Arbitrario (1932) N. Cimento, 9, pp. 335-344Maris, H., On the Fission of Elementary Particles and Evidence for Fractional Electrons in Liquid Helium (2000) J. Low Temp. Phys, 120, pp. 173-204Naber, G.L., (2000) Topology, Geometry and Gauge Fields. Interactions, , Appl. Math. Sci. 141, Springer-Verlag, New YorkNicolescu, L.I., (2000) Notes on Seiberg-Witten Theory, , Graduate Studies in Mathematics 28, Am. Math. Soc, Providence, Rohde IslandNash, C., Sen, S., (1983) Topology and Geometry for Physicists, , Academic Press, LondonOliveira, Capelas de, E., Rodrigues Jr., W.A., (2007) Subluminal, Luminal and Superluminal Wave Motion, , Book in preparationRainich, G., Electrodynamics and General Relativity Theory (1925) Am. Math. Soc. Trans, 27, pp. 106-136Rodrigues Jr., W.A., Lu, J.Y., On the Existence of Undistorted Progressive Waves (UPWs) of Arbitrary Speeds 0 ≤ = v ≤ ∞ in Nature (1997) Found. Phys, 27, pp. 435-508Rodrigues Jr., W.A., Tiomno, J., On Experiments to Detect Possible Failures of Relativity Theory (1985) Found. Phys, 15, pp. 995-961. , Not citedRodrigues, W. A. Jr., and Vaz, J. Jr, Subluminal and Superluminal Solutions in Vacuum of the Maxwell Equations and the Massless Dirac Equation. Talk presented at the International Conference on the Theory of the Electron, Mexico City, 1995, Advances in Appl. Clifford Algebras 7 (Sup.), 453-462 (1997)Rodrigues Jr., W.A., Vaz, Jr., From Electromagnetism to Relativistic Quantum Mechanics (1998) Found. Phys, 28, pp. 789-814Rodrigues Jr., W.A., Maiorino, J.E., A Unified Theory for Construction of Arbitrary Speeds (0 ≤ = v ≤ ∞) Solutions of the Relativistic Wave Equations (1996) Random Oper. Stochastic Equ, 4, pp. 355-400Rodrigues, W. A. Jr., The Relation between Dirac, Maxwell and Seiberg-Witten Equations, Int. J. Mathematics and Mathematical Sci. 2003, 2707-2734 (2003). [math-ph/0212034]Sachs, M., (1982) General Relativity and Matter, p. 373. , D. Reidel, DordrechtSallhöfer, H., Elementary Derivation of the Dirac Equations. X (1986) Zeitschrift für Naturforschung, 41 a, pp. 468-470Sallhöfer, H., Maxwell-Dirac-Isomorphism. XI (1986) Zeitschrift für Naturforschung, 41 a, pp. 1087-1088Sallhöfer, H., Maxwell-Dirac-Isomorphism. XII (1986) Zeitschrift für Naturforschung, 41 a, pp. 1335-1336Sallhöfer, H., Maxwell-Dirac-Isomorphism. XI (1986) Zeitschrift für Naturforschung, 41 a, pp. 1431-1432Seiberg, N. and Witten, E. Monopoles, Duality and Chiral Symmetry Breaking in N = 2 QCD, Nucl. Phys. B 431, 581-640 (1994)Silverman, M.P., (1998) Waves and Grains, , Princeton University Press, PrincetonSimulik, V.M., Krivisshi, I.Y., Slight Generalized Maxwell Classical Electrodynamics can be Applied to Inneratomic Phenomena (2002) Ann. Fond. L. de Broglie, 27, pp. 303-328Vaz Jr., J., Clifford Algebras and Witten's Monopole Equations (1997) Geometry, Topology and Physics, , Apanasov, B. N, Bradlow, S. B, Rodrigues, W. A. Jr. and Uhlenbeck, K. K, eds, W. de Gruyter, BerlinVaz Jr., J., Rodrigues Jr., W.A., On the Equivalence of Maxwell and Dirac Equations and Quantum Mechanics (1993) Int. J. Theor. Phys, 32, pp. 945-958Vaz, J. Jr., and Rodrigues,W. A. Jr., Maxwell and Dirac Theories as an Already Unified Theory. Talk presented at the International Conference on the Theory of the Electron, Mexico City, 1995, Advances in Appl. Clifford Algebras 7 (Sup.), 369-386 (1997
The Maxwell And Navier-stokes Equations That Follow From Einstein Equation In A Spacetime Containing A Killing Vector Field
No full textConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this paper we are concerned to reveal that any spacetime structure 〈M, g, D, τg, ↑〉, which is a model of a gravitational field in General Relativity generated by an energy-momentum tensor T - and which contains at least one nontrivial Killing vector field A - is such that the 2-form field F = dA (where A = g(A,)) satisfies a Maxwell like equation - with a well determined current that contains a term of the superconducting type- which follows directly from Einstein equation. Moreover, we show that the resulting Maxwell like equations, under an additional condition imposed to the Killing vector field, may be written as a Navier-Stokes like equation as well. As a result, we have a set consisting of Einstein, Maxwell and Navier-Stokes equations, that follows sequentially from the first one under precise mathematical conditions and once some identifications about field variables are evinced, as explained in details throughout the text. We compare and emulate our results with others on the same subject appearing in the literature. In Appendix A we fix our notation and recall some necessary material concerning the theory of differential forms, Lie derivatives and the Clifford bundle formalism used in this paper. Moreover, we comment in Appendix B on some analogies (and main differences) between our results to the ones obtained long ago by Bergmann and Kommar which are reviewed and briefly criticized. © 2012 American Institute of Physics.1483277295Cons. Nac. Desenvolv. Cient. Tecnol. (CNPq),Coordenacao Aperfeicoamento Pessoal Nivel Super. (CAPES),Fund. Amparo Pesqui. Estado Rio de Janeiro (FAPERJ),International Centre for Theoretical Physics (ICTP),Centro Latino Americano de Fisica (CLAF)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Bhattacharyya, S., Hubeny, V.E., Minwalla, S., Rangamani, M., (2008) JHEP, 2, p. 045. , arXiv:0712. 2456 [hep-th]]Bhattacharyya, S., Minwalla, S., Wadia, S.R., (2009) JHEP, 8, p. 059. , arXiv:0810. 1545 [hep-th]]Bergmann, P.G., (1958) Phys. Rev., 112, pp. 287-289Breedberg, I., Keller, C., Lysov, V., Strominger, A., arXiv: 1101. 2451 [hep-ph]]Chorin, A.J., Marsden, J.E., A Mathematical Introduction to Fluid Mechanics, p. 1993. , Springer-Verlag, New-YorkDa Rocha, R., Rodrigues Jr., W.A., (2010) J. Phys. A: Math. Theor., 43, p. 205206. , arXiv:0910. 2021 [math-ph]]Da Rocha, R., Rodrigues Jr., W.A., (2008) Adv. Appl. Clifford Alg., 18, pp. 351-367. , arXiv:mathph/ 0510026]Eling, C., Fouxon, I., Oz, Y., arXiv:1004. 2632 [hep-th]]Fayos, F., Sopuerta, C.F., (2002) Class. Quant. Grav., 19, pp. 5489-5505. , arXiv:gr-qc/0205098]Fernandez, V.V., Rodrigues Jr., W.A., (2010) Gravitation As A Plastic Distortion of the Lorentz Vacuum, Fundamental Theories of Physics, 168. , Springer, HeidelbergFlanders, H., (1963) Differential Forms with Applications to the Physical Sciences, , Academic Press, New YorkGiglio, J.F.T., Rodrigues Jr., W.A., (2012) Annalen der Physik, 524, pp. 302-310. , arXiv:1111. 2206 [math-ph]]Geroch, R., (1968) J. Math. Phys., 9, pp. 1739-1744Hubney, V.E., (2011) Class. Quant. Grav., 28, p. 114007. , arXiv:1011. 4948 [gr-qc]]Komar, A., (1958) Phys. Rev., 113, pp. 934-936Landau, L.D., Lifshitz, E.M., The Classical Theory of Fields, p. 1975. , Pergamon Press, New YorkMarmanis, H., (1998) Phys. of Fluids, 10, pp. 1428-1437Misner, C.W., Thorne, K.S., Wheeler, J.A., Gravitation, p. 1973. , W. H. Freeman. and Co. , San FranciscoMosna, R.A., Miralles, D., Vaz Jr., J., (2003) J. Phys. A, 36, pp. 4395-4405. , arXiv:math-ph/0212020]Notte-Cuello, E., Da Rocha, R., Rodrigues Jr., W.A., (2010) J. Phys. Math. 2, pp. P100506. , arXiv:0907. 2424 [math-ph]]Padmanabhan, T., (2011) Int. J. Mod. Phys. D, 20, pp. 2817-2822Papapetrou, A., (1966) Ann. de L'I. Henri Poincaré, Section A, 4, pp. 83-105Rangamani, M., (2009) Class. Quant. Grav., 26, p. 224003. , arXiv:0905. 4352 [hep-th]]Rodrigues Jr., W.A., Capelas De Oliveira, E., (2007) The Many Faces of Maxwell, Dirac and Einstein Equations. A Clifford Bundle Approach, Lecture Notes in Physics, p. 722. , Springer, HeidelbergRodrigues Jr., W.A., (2010) Adv. Appl. Clifford Alg., 20, pp. 871-884Rodrigues Jr., W.A., (2012) Rep. Math. Phys., 69, pp. 265-279. , arXiv:1109. 5272v3 [math-ph]]Sanchez, M., (1977) Nonlinear Analysis, Meth. Applications, 30, pp. 634-654Sachs, R.K., Wu, H., General Relativity for Mathematicians, p. 1977. , Springer-Verlag, New YorkSchmelzer, I., (2012) Adv. Appl. Clifford Alg., 22, pp. 203-242. , arXiv:gr-qc/0205035]Sulaiman, A., Handoko, L.T., (2009) Int. J. Mod. Phys. A, 24, pp. 3630-3637. , arXiv:physics/0508219 [physics. flu-dyn]]Sulaiman, A., Djun, T.P., Handoko, L.T., (2006) J. Theor. Comput. Stud., 5, p. 0401. , arXiv:physics/0508086 [physics. flu-dyn]]Wald, R.M., General Relativity, p. 1984. , University of Chicago Press, ChicagoWeinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, p. 1972. , J. Wiley & Sons, Inc. , New Yor
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