2,367 research outputs found
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
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
A Comment On: 'on Some Contradictory Computations In Multi-dimensional Mathematics'
No full textIn this paper we analyze the status of some 'unbelievable results' presented in the paper 'On Some Contradictory Computations in Multi-Dimensional Mathematics' [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725-734] published in Nonlinear Analysis, a journal indexed in the Science Citation Index. Among some of the unbelievable results 'proved' in the paper we can find statements like: (i) a rotation T θ : R 2 → R 2, θ ≠ n π / 2, is inconsistent with arithmetic, (ii) complex number theory is inconsistent. Besides these 'results' of mathematical nature, [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725-734] offers also a 'proof' that Special Relativity is inconsistent. Now, we are left with only two options (a) the results of [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725-734] are correct and in this case we need a revolution in Mathematics (and also in Physics) or (b) the paper is a potpourri of nonsense. We show that option (b) is the correct one. All 'proofs' appearing in [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725-734] are trivially wrong, being based on a poor knowledge of advanced calculus notions. There are many examples (some of them discussed in [A.L.T. Carvalho, W.A. Rodrigues Jr., The non sequitur mathematics and physics of the 'new electrodynamics' proposed by the AIAS group, Random Oper. Stoch. Equs. 9 (2001) 161-206. http://arxiv.org/abs/physics/0302016; E. Capelas de Oliveira, W.A. Rodrigues Jr., Dotted and undotted algebraic spinor fields in general relativity, Int. J. Mod. Phys. D 13 (2004) 1637-1659. http://arxiv.org/abs/math-ph/0407024; W.A. Rodrigues Jr., E. Capelas de Oliveira, Clifford valued differential forms and some issues on gravitation, electromagnetism and "unified" theories, Int. J. Mod. Phys. D 13 (2004) 1879-1915. http://arxiv.org/abs/math-ph/0407025; W.A. Rodrigues Jr., Q.A.G. Souza, An ambiguous statement called 'tetrad postulate' and the correct field equations satisfied by the tetrad fields, Int. J. Mod. Phys. D 14 (2005) 2095-2150. http://arxiv.org/abs/math-ph/0411085; W.A. Rodrigues Jr., A comment on Emergent Gravity, http://arxiv.org/abs/gr-qc/0602111]) of completely wrong papers using non sequitur Mathematics in the Physics literature. Taking into account also that a paper like [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725-734] appeared in a Mathematics journal we think that it is time for editors and referees of scientific journals to become more careful in order to avoid the dissemination of nonsense. © 2006 Elsevier Ltd. All rights reserved.67723162320Carvalho, L.A.V., On some contradictory computations in multi-dimensional mathematics (2005) Nonlinear Anal., 63, pp. 725-734Carvalho, A.L.T., Rodrigues Jr., W.A., The non sequitur mathematics and physics of the 'new electrodynamics' proposed by the AIAS group (2001) Random Oper. Stoch. Equs., 9, pp. 161-206. , http://arxiv.org/abs/physics/0302016Capelas de Oliveira, E., Rodrigues Jr., W.A., Dotted and undotted algebraic spinor fields in general relativity (2004) Int. J. Mod. Phys. D., 13, pp. 1637-1659. , http://arxiv.org/abs/math-ph/0407024Rodrigues Jr., W.A., Capelas de Oliveira, E., Clifford valued differential forms and some issues on gravitation, electromagnetism and "unified" theories (2004) Int. J. Mod. Phys. D., 13, pp. 1879-1915. , http://arxiv.org/abs/math-ph/0407025Rodrigues Jr., W.A., Souza, Q.A.G., An ambiguous statement called 'tetrad postulate' and the correct field equations satisfied by the tetrad fields (2005) Int. J. Mod. Phys. D., 14, pp. 2095-2150. , http://arxiv.org/abs/math-ph/0411085Rodrigues Jr., W.A., A Comment on Emergent Gravity, , http://arxiv.org/abs/gr-qc/0602111Spiegel, M.R., (1963) Advanced Calculus, , Schaum Publ. Co, New Yor
Multiform And Extensor Calculus
No full text[No abstract available]7221960Ablamowicz, R., Lounesto, P., Maks, J., Conference Report: Second Workshop on Clifford Algebras and their Applications in Mathematical Physics (1991) Found. Phys, 21, pp. 735-748Arcuri, R.C., Conformal and Critical Embedding, Infinite Magic Square and a New Clifford Product (1991) J. Math. Phys, 32, pp. 1890-1899Crumeyrolle, A., (1990) Orthogonal and Sympletic Clifford Algebras, , Kluwer Acad. Publ, DordrechtFernández, 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]Frankel, T., (1997) The Geometry of Physics, , Cambridge University Press, CambridgeHestenes, D., Sobczyk, G., (1984) Clifford Algebra to Geometric Calculus, , D. Reidel Publ. Co, DordrechtLawson, 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., (1997) Clifford Algebras and Spinors, , Cambridge Univ. Press, CambridgeMoya, 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 Functionals, Adv. Appl. Clifford Algebras 11, 93-103 (2001). [math.GM/0212224]Rodrigues, W. A. Jr., and Oliveira, E. Capelas de, A Comment on the Twin Paradox and the Hafele-Keating Experiment, Phys. Lett. A 140 479-484 (1989)Rodrigues Jr., W.A., Rosa, M.A.F., The Meaning of Time in Relativity and Einstein's Later View of the Twin Paradox (1989) Found. Phys, 19, pp. 705-72
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
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
Compsoneura rigidifolia W.A. Rodrigues from Colombia collected by J. Cabezas #1466
No full textFile Name: TOLI-26349-AMA-01-B17-04.jpg
CÓDIGO FOTO: TOLI-26349-AMA-01-B17-04-
Fotografía: SI
Nº TOLI: TOLI-26349
PARCELA: AMA-01
CÓDIGO: B17-4
Nº COLECTA: 1466
NUEVOS COLECTORES: Jaime Andrés Cabezas
COLECTORES: J. Cabezas
Nº MUESTRAS MONTADAS: 1
Homologación: Homologado
Nueva fecha del evento : 27/11/2018.
Fecha del evento: 27/11/2018.
Proyecto : Recursos Botánicos Disponibles en Línea (BRAVO) para la flora Colombiana
Hábitat: Bosque muy húmedo tropical (bmh-T)
Comentario del evento: Bosque de tierra firme
Continente: SA
Pais: Colombia
Estado/Provincia: Chocó
Municipio: Nuquí
Centro poblado / Cabecera municipal: Arusí
Localidad: Reserva Natural El Amargal
Elevación minima en metros: 50
Elevación maxima en metros: 300
Latitud: 5.578
Longitud original: -77.500
datum geodésico: WGS 84
Latitud decimal: 5.578
Longitud decimal: -77.500
Familia antigua: Myristicaceae
Especie antigua: Compsoneura rigidifolia
Nombre cientifico: Compsoneura rigidifolia W.A. Rodrigues
Reino: Plantae
Filo: Magnoliophyta
Clase: Equisetopsida
Familia nueva: Myristicaceae
Género nuevo: Compsoneura
especie nueva: rigidifolia
Autoría del nombre científico: W.A. Rodrigues
genero herbario: Compsoneura
especie herbario: rigidifolia
Especie de herbario para TNRS: Compsoneura rigidifolia
Especie corregida herbario y desde TNRS: Compsoneura rigidifolia
Familia corregida desde TNRS: Myristicaceae
: 5333</p
Virola marleneae W.A. Rodrigues from Colombia collected by F. Moreno y C. Carvajal #366
No full textFile Name: TOLI-21904-PER-01-D5
CÓDIGO FOTO: TOLI-21904-PER-01-D5
Fotografía: SI
Nº TOLI: TOLI-21904
PARCELA: PER-01
CÓDIGO: D5
Nº COLECTA: 366
NUEVOS COLECTORES: Esteban Álvarez Dávila
COLECTORES: F. Moreno y C. Carvajal
Nº MUESTRAS MONTADAS: 1
Homologación: Homologado
Nueva fecha del evento : 20/12/2018.
Fecha del evento: 01/09/2012.
Proyecto : Recursos Botánicos Disponibles en Línea (BRAVO) para la flora Colombiana
Hábitat: Bosque húmedo tropical (bh-T)
Comentario del evento: Bosque de tierra firme, dosel abierto, de 25-30 m, emergentes de 35 m, estrato medio de 15 m, sotobosque denso con alta regeneración natural, presencia de palmas como Lepidocaryum tenue, Oenocarpus bataua, Geonoma sp., capa de hojarazca de 15 cm, abundante materia orgánica. Pendientes pronunciadas. Poca intervención antrópica.
Continente: SA
Pais: Colombia
Estado/Provincia: Amazonas
Municipio: Puerto Santander
Localidad: Resguardo indígena Nonuya de Villazul.
Elevación minima en metros: 250
Elevación maxima en metros: 400
Latitud: -0.654
Longitud original: -72.072
datum geodésico: WGS 84
Latitud decimal: -0.654
Longitud decimal: -72.072
Identificado por: Boris Villanueva
Fecha de identificación: 26/01/2019.
Familia antigua: Myristicaceae
Especie antigua: Virola pavonis (A. DC.) A.C. Sm.
Nombre cientifico: Virola marleneae W.A. Rodrigues
Reino: Plantae
Filo: Magnoliophyta
Clase: Equisetopsida
Orden: Magnoliales
Familia nueva: Myristicaceae
Género nuevo: Virola
especie nueva: marleneae
Autoría del nombre científico: W.A. Rodrigues
: Myristicaceae
genero herbario: Virola
especie herbario: marleneae
Especie de herbario para TNRS: Virola marleneae
Especie corregida herbario y desde TNRS: Virola marlenei
Familia corregida desde TNRS: Myristicaceae
: 1045</p
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
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