RELATIVISTIC PARTICLE WITH CURVATURE IN AN EXTERNAL ELECTROMAGNETIC FIELD

1991 ◽  
Vol 06 (22) ◽  
pp. 3989-3996 ◽  
Author(s):  
V.V. NESTERENKO
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Phase Space ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Canonical Quantization ◽  
Hamiltonian Formalism ◽  
External Electromagnetic Field ◽  
Operator Form ◽  
Complete Set

A model of a relativistic particle with curvature interacting with an external electromagnetic field in a “minimal way” is investigated. The generalized Hamiltonian formalism for this model is constructed. A complete set of the constraints in the phase space is obtained and then divided into first- and second-class constraints. On this basis the canonical quantization of the model is considered. A wave equation in the operator form, resembling the Dirac equation in an external electromagnetic field, is obtained. The massless version of this model is briefly discussed.

scholarly journals The Non-Relativistic Limit of the DKP Equation in Non-Commutative Phase-Space

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 223 ◽  
Author(s):  
Ilyas Haouam
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Dirac Equation ◽  
Linear Transformation ◽  
Canonical Transformation ◽  
External Electromagnetic Field ◽  
Pauli Equation ◽  
Relativistic Limit ◽  
Dkp Equation ◽  
Commutation Relations

The non-relativistic limit of the relativistic DKP equation for both of zero and unity spin particles is studied through the canonical transformation known as the Foldy–Wouthuysen transformation, similar to that of the case of the Dirac equation for spin-1/2 particles. By considering only the non-commutativity in phases with a non-interacting fields case leads to the non-commutative Schrödinger equation; thereafter, considering the non-commutativity in phase and space with an external electromagnetic field thus leads to extract a phase-space non-commutative Schrödinger–Pauli equation; there, we examined the effect of the non-commutativity in phase-space on the non-relativistic limit of the DKP equation. However, with both Bopp–Shift linear transformation through the Heisenberg-like commutation relations, and the Moyal–Weyl product, we introduced the non-commutativity in phase and space.

Singularities of electron kernel functions in an external electromagnetic field

1954 ◽  
Vol 222 (1148) ◽  
pp. 93-108 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Wave Equation ◽  
Vacuum Polarization ◽  
Proper Time ◽  
External Electromagnetic Field ◽  
Kernel Functions ◽  
Second Order ◽  
Significant Part ◽  
Second Order Wave Equation

The electron kernel functions are derived from solutions of the second-order wave equation, using the proper-time parametrization. Iterated kernel functions are introduced and a gauge-independent perturbation theory is developed. The separation of singular parts proceeds in terms of the iterated kernel functions valid in the absence of an electromagnetic field, and the singular expressions which have to be compensated in order to determine the physically significant part of the vacuum polarization are obtained in a more transparent form than those given originally by Heisenberg.

Semiclassical Form of the Relativistic Particle Propagator

1997 ◽  
Vol 12 (32) ◽  
pp. 2435-2443
Author(s):  
Dmitri M. Gitman ◽  
Stoian I. Zlatev
Keyword(s):  
Electromagnetic Field ◽  
Relativistic Particle ◽  
External Electromagnetic Field ◽  
Path Integral Representation ◽  
Constant Electromagnetic Field ◽  
Final Formula ◽  
Nonrelativistic Quantum Mechanics ◽  
Van Vleck ◽  
Detailed Derivation ◽  
Particle Propagator

A detailed derivation of the semiclassical form for the relativistic particle propagator in arbitrary external electromagnetic field is presented. To this end a path-integral representation is used. The final formula is a generalization of the Van Vleck–Pauli–Morette semiclassical representation in the nonrelativistic quantum mechanics. We demonstrate the efficiency of the former in the case of an arbitrary constant electromagnetic field.

scholarly journals GEOMETRIC STRUCTURES OF THE CLASSICAL GENERAL RELATIVISTIC PHASE SPACE

2008 ◽  
Vol 05 (05) ◽  
pp. 699-754 ◽  
Author(s):  
JOSEF JANYŠKA ◽  
MARCO MODUGNO
Keyword(s):  
Electromagnetic Field ◽  
Phase Space ◽  
Relativistic Particle ◽  
Jet Space ◽  
Geometric Structures ◽  
Geometric Properties ◽  
Geometric Conditions ◽  
General Relativistic ◽  
Relativistic Phase

This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1-dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the geometric conditions by which the Lorentz metric and a connection of the phase space yield contact and Jacobi structures. In particular, we specialize these conditions to the cases when the connection of the phase space is generated by the metric and an additional tensor. Indeed, the case generated by the metric and the electromagnetic field is included, as well.

scholarly journals CANONICAL QUANTIZATION OF THE BELINSKIĬ-ZAKHAROV ONE-SOLITON SOLUTIONS

1995 ◽  
Vol 04 (06) ◽  
pp. 749-766
Author(s):  
NENAD MANOJLOVIC ◽  
GUILLERMO A. MENA MARUGÁN
Keyword(s):  
Phase Space ◽  
Quantum Dynamics ◽  
Canonical Quantization ◽  
Soliton Solutions ◽  
Irreducible Unitary Representation ◽  
Einstein Equations ◽  
Classical Solutions ◽  
Hamiltonian Constraint ◽  
Dynamical Equations ◽  
Complete Set

We apply the algebraic quantization programme proposed by Ashtekar to the analysis of the Belinskiĭ-Zakharov classical spacetimes, obtained from the Kasner metrics by means of a generalized soliton transformation. When the solitonic parameters associated with this transformation are frozen, the resulting Belinskiĭ-Zakharov metrics provide the set of classical solutions to a gravitational minisuperspace model whose Einstein equations reduce to the dynamical equations generated by a homogeneous Hamiltonian constraint and to a couple of second-class constraints. The reduced phase space of such a model has the symplectic structure of the cotangent bundle over R+×R+. In this reduced phase space, we find a complete set of real observables which form a Lie algebra under Poisson brackets. The quantization of the gravitational model is then carried out by constructing an irreducible unitary representation of that algebra of observables. Finally, we show that the quantum theory obtained in this way is unitarily equivalent to that which describes the quantum dynamics of the Kasner model.

Sign in / Sign up

Export Citation Format

Share Document