scholarly journals Algebra of Symmetry Operators for Klein-Gordon-Fock Equation

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 727
Author(s):  
Valeriy V. Obukhov
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Riemannian Space ◽  
Space Time ◽  
First Order ◽  
External Electromagnetic Fields ◽  
Klein Gordon ◽  
Symmetry Operators ◽  
Algebra Of Operators

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time V4 a group of motion G3 acts simply transitively on a non-null subspace of transitivity V3. It is shown that in the case of a Riemannian space Vn, in which the group Gr acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group Gr.

Algebras of symmetry operators of Klein-Gordon-Fock equation for groups acting transitively on two-dimensional subspaces of space-time manifold

2021 ◽  
pp. 126-131
Author(s):  
V.V. Obukhov ◽  
◽  
K.R Myrzakulov ◽  
U.A. Guselnikova ◽  
A. Zhadyranova ◽  
...  
Keyword(s):  
Electromagnetic Fields ◽  
Test Particle ◽  
Dimensional Subspace ◽  
Two Dimensional ◽  
First Order ◽  
External Electromagnetic Fields ◽  
Klein Gordon ◽  
Symmetry Operators ◽  
Charged Test Particle ◽  
Charged Test

All external electromagnetic fields are found in which the Klein-Gordon-Fock equation for a charged test particle admits first-order symmetry operators provided that the groups G 3, r £ 3, of motions act transitively on the two-dimensional subspace V 2.

FREE ELECTROMAGNETIC FIELD IN RIEMANNIAN SPACE-TIME via DKP THEORY

2002 ◽  
Vol 17 (29) ◽  
pp. 4197-4202 ◽  
Author(s):  
R. CASANA ◽  
B. M. PIMENTEL ◽  
J. T. LUNARDI ◽  
R. G. TEIXEIRA
Keyword(s):  
Electromagnetic Field ◽  
Riemannian Space ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Space Time ◽  
Dkp Equation ◽  
Massless Spin ◽  
Free Electromagnetic Field

We study the massless Duffin-Kemmer-Petiau (DKP) equation in Riemannian space-times, particularly the massless spin 1 sector which reproduces the free Maxwell's equations.

scholarly journals EFFECTIVE DYNAMICS FOR SOLITONS IN THE NONLINEAR KLEIN–GORDON–MAXWELL SYSTEM AND THE LORENTZ FORCE LAW

2009 ◽  
Vol 21 (04) ◽  
pp. 459-510 ◽  
Author(s):  
EAMONN LONG ◽  
DAVID STUART
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Force ◽  
Scalar Fields ◽  
Space Time ◽  
Maxwell System ◽  
Complex Scalar ◽  
Effective Dynamics ◽  
Dimensional Minkowski Space ◽  
Klein Gordon ◽  
Lorentz Force Law

We consider the nonlinear Klein–Gordon–Maxwell system derived from the Lagrangian [Formula: see text] on four-dimensional Minkowski space-time, where ϕ is a complex scalar field and Fμν = ∂μ𝔸ν - ∂ν𝔸μ is the electromagnetic field. For appropriate nonlinear potentials [Formula: see text], the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and studied by Lee and collaborators for pure complex scalar fields. In this article, we develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main theorems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field produced by the background current 𝕁B, and compute their effective dynamics to O(e). The effective dynamical equation is the equation of motion for a relativistic particle acted on by the Lorentz force law familiar from classical electrodynamics. The theorems are valid in a scaling regime in which the external electromagnetic fields are O(1), but vary slowly over space-time scales of [Formula: see text], and δ = e1 - k for [Formula: see text] as e → 0. We work entirely in the energy norm, and the approximation is controlled in this norm for times of [Formula: see text].

scholarly journals On Tubes of Force in a special class of electromagnetic fields

1922 ◽  
Vol 41 ◽  
pp. 100-107
Author(s):  
G. S. Eastwood
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Electromagnetic Force ◽  
Special Class ◽  
Royal Society ◽  
Space Time ◽  
The Other ◽  
Family Meeting ◽  
The One

Professor Whittaker, in a paper entitled “On Tubes of Electromagnetic Force” {see Proceedings of the Royal Society of Edinburgh, Vol. XLII., Part I. (No 1)}, introduces certain surfaces, which he names calamoids, in connection with an electromagnetic field in the four-dimensional world of space-time. The calamoids consist of “a convariant family of surfaces which when the field is purely electrostatic or purely magnetostatic reduce to the ordinary Faraday tubes of force.” Professor Whittaker, in the paper referred to, also introduces two sets of surfaces, each a covariant family of ∞2 surfaces, one of them named the electropotential surfaces, and the other family the magnetopotential surfaces of the electromagnetic field. The electropotential surfaces and the magnetopotential surfaces are shown to be everywhere absolutely orthogonal. (One member of each family meeting at a point, any line from this point in the one family is orthogonal to every line through the point in the other family). Moreover, a “calamoid, at every one of its points, is half-parallel and half-orthogonal to the electropotential surface which passes through the point, and is also half-parallel and half-orthogonal to the magnetopotential surface which passes through the point.”

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