1,721,133 research outputs found
On the phase-integral method for the radial Dirac equation
Get PDFIn the application of potential models, the use of the Dirac equation in central potentials remains of phenomenological interest. The associated set of decoupled second-order ordinary differential equations is here studied by exploiting the phase-integral technique, following the work of Froman and Froman that provides a powerful tool in ordinary quantum mechanics. For various choices of the scalar and vector parts of the potential, the phase-integral formulae are derived and discussed, jointly with formulae for the evaluation of Stokes and anti-Stokes lines. A criterion for choosing the base function in the phase-integral method is also obtained, and tested numerically. The case of scalar confinement is then found to be more tractable
Qualitative properties of the Dirac equation in a central potential
Get PDFThe Dirac equation for a massive spin-1/2
field in a central potential V in three
dimensions is studied without fixing a priori the functional form of V . The second-order equations
for the radial parts of the spinor wavefunction are shown to involve a squared Dirac operator for
the free case, whose essential self-adjointness is proved by using the Weyl limit point-limit circle
criterion, and a ‘perturbation’ resulting from the potential. One then finds that a potential of
Coulomb type in the Dirac equation leads to a potential term in the above second-order equations
which is not even infinitesimally form-bounded with respect to the free operator. Moreover, the
conditions ensuring essential self-adjointness of the second-order operators in the interacting case
are changed with respect to the free case, i.e. they are expressed by a majorization involving
the parameter in the Coulomb potential and the angular momentum quantum number. The same
methods are applied to the analysis of coupled eigenvalue equations when the anomalous magnetic
moment of the electron is not neglected
Supplementary Video 2 - Supplemental material for Zone 1 Debranching for Frozen Elephant Trunk and Whole-Body Perfusion
No full textSupplemental material, Supplementary Video 2, for Zone 1 Debranching for Frozen Elephant Trunk and Whole-Body Perfusion by Gianluigi Bisleri, Syed M. Ali Hassan, Darrin M. Payne, Dimitri Petsikas, Andrew Hamilton, and Giampiero Esposito in Innovations: Technology and Techniques in Cardiothoracic and Vascular Surgery</p
Supplementary Video 1 - Supplemental material for Zone 1 Debranching for Frozen Elephant Trunk and Whole-Body Perfusion
No full textSupplemental material, Supplementary Video 1, for Zone 1 Debranching for Frozen Elephant Trunk and Whole-Body Perfusion by Gianluigi Bisleri, Syed M. Ali Hassan, Darrin M. Payne, Dimitri Petsikas, Andrew Hamilton, and Giampiero Esposito in Innovations: Technology and Techniques in Cardiothoracic and Vascular Surgery</p
Coleman-Weinberg SO(10) grand unified theories as inflationary models
No full textThe flat-space limit of the one-loop effective potential for SO(10) GUT’s in spatially flat Friedmann-
Robertson-Walker cosmologies is applied to study the dynamics of the early universe. The numerical integration
of the corresponding field equations shows that, for such grand unified theories, a sufficiently long
inflationary stage is achieved for suitable choices of the initial conditions. However, a severe fine-tuning of
these initial conditions is necessary to obtain a large e-fold number. In the direction with residual symmetry
SU(4)PS SU(2)L SU(2)R, one eventually finds parametric resonance for suitable choices of the free parameters
of the classical potential. This phenomenon leads in turn to the end of inflatio
A Non-Singular One-Loop Wave Function of the Universe From a New Eigenvalue Asymptotics in Quantum Gravity
No full textRecent work on Euclidean quantum gravity on the four-ball has proved regularity at the origin of the generalized zeta-function built from eigenvalues for metric and ghost modes, when diffeomorphism-invariant boundary conditions are imposed in the de Donder gauge. The hardest part of the analysis involves one of the four sectors for scalar-type perturbations, the eigenvalues of which are obtained by squaring up roots of a linear combination of Bessel functions of integer adjacent orders, with a coefficient of linear combination depending on the unknown roots. This paper obtains, first, approximate analytic formulae for such roots for all values of the order of Bessel functions. For this purpose, both the descending series for Bessel functions and their uniform asymptotic expansion at large order are used. The resulting generalized zeta-function is also built, and another check of regularity at the origin is obtained. For the first time in the literature on quantum gravity on manifolds with boundary, a vanishing one-loop wave function of the Universe is found in the limit of small three-geometry, which suggests a quantum avoidance of the cosmological singularity driven by full diffeomorphism invariance of the boundary-value problem for one-loop quantum theory
Quantum effects in Friedmann - Robertson - Walker cosmologies
Get PDFElectrodynamics for self-interacting scalar fields in spatially flat Friedmann–
Robertson–Walker spacetimes is studied. The corresponding 1-loop field equation for the
expectation value of the complex scalar field in the conformal vacuum is derived. For
exponentially expanding universes, the equations for the Bogoliubov coefficients describing the
coupling of the scalar field to gravity are solved numerically. They yield a non-local correction
to the Coleman–Weinberg effective potential which does not modify the pattern of minima found
in static de Sitter space. Such a correction contains a dissipative term which, accounting for the
decay of the classical configuration in scalar field quanta, may be relevant for the reheating stage.
The physical meaning of the non-local term in the semiclassical field equation is investigated
by evaluating this contribution for various background field configurations
Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions
No full textA general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding one-loop divergences and one-loop effective action actually exists. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity are affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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