Algebra of the Symmetry Operators of the Klein-Gordon-Fock Equation for the Case When Groups of Motions G3 Act Transitively on Null Subsurfaces of Spacetime

@article{Obukhov2022AlgebraOT,
  title={Algebra of the Symmetry Operators of the Klein-Gordon-Fock Equation for the Case When Groups of Motions G3 Act Transitively on Null Subsurfaces of Spacetime},
  author={Valery V. Obukhov},
  journal={Symmetry},
  year={2022},
  volume={14},
  pages={346}
}
  • V. Obukhov
  • Published 25 January 2022
  • Mathematics
  • Symmetry
The algebras of the symmetry operators for the Hamilton–Jacobi and Klein–Gordon–Fock equations are found for a charged test particle, moving in an external electromagnetic field in a spacetime manifold on the isotropic (null) hypersurface, of which a three-parameter groups of motions acts transitively. We have found all admissible electromagnetic fields for which such algebras exist. We have proved that an admissible field does not deform the algebra of symmetry operators for the free Hamilton… 

Algebras of integrals of motion for the Hamilton–Jacobi and Klein–Gordon–Fock equations in spacetime with four-parameter groups of motions in the presence of an external electromagnetic field

  • V. Obukhov
  • Mathematics
    Journal of Mathematical Physics
  • 2022
The algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are

Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields

Maxwell’s vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of

Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe

For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer

Family of Asymptotic Solutions to the Two-Dimensional Kinetic Equation with a Nonlocal Cubic Nonlinearity

We apply the original semiclassical approach to the kinetic ionization equation with the nonlocal cubic nonlinearity in order to construct the family of its asymptotic solutions. The approach

Gravitational wave of the Bianchi VII universe: particle trajectories, geodesic deviation and tidal accelerations

For the gravitational wave model based on the type III Shapovalov wave space-time, test particle trajectories and the exact solution of geodesic deviation equations for the Bianchi type VII universe

References

SHOWING 1-10 OF 34 REFERENCES

Algebras of integrals of motion for the Hamilton–Jacobi and Klein–Gordon–Fock equations in spacetime with four-parameter groups of motions in the presence of an external electromagnetic field

  • V. Obukhov
  • Mathematics
    Journal of Mathematical Physics
  • 2022
The algebras of the integrals of motion of the Hamilton-Jacobi and Klein-Gordon-Fock equations for a charged test particle moving in an external electromagnetic field in a spacetime manifold are

Algebra of symmetry operators for Klein-Gordon-Fock equation

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

Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups

We investigate the structure of the Klein-Gordon-Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We show that in the

Separation of variables in Hamilton–Jacobi and Klein–Gordon–Fock equations for a charged test particle in the stackel spaces of type (1.1)

All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that Hamilton-Jacobi equation and Klein-Gordon-Fock equation for a charged test particle can

Constructing a Complete Integral of the Hamilton–Jacobi Equation on Pseudo-Riemannian Spaces with Simply Transitive Groups of Motions

In this work, a method for constructing a complete integral of the geodesic Hamilton-Jacobi equation on pseudo-Riemannian manifolds with simply transitive actions of groups of motions is suggested.

Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces

The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups.

Schrödinger Equations in Electromagnetic Fields: Symmetries and Noncommutative Integration

An algorithm for constructing the first-order symmetry algebra is presented and its structure is described in terms of Lie algebra central extensions and the original Schrödinger equation was reduced to an ordinary differential equation using the noncommutative integration method developed by Shapovalov and Shirokov.

Complete separability of the Hamilton–Jacobi equation for the charged particle orbits in a Liénard–Wiechert field

We classify all orthogonal coordinate systems in M4, allowing complete additively separated solutions of the Hamilton–Jacobi equation for a charged test particle in the Lienard–Wiechert field

Hamilton-Jacobi Equation for a Charged Test Particle in the Stäckel Space of Type (2.0)

All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete

Orthogonal Separation of the Hamilton-Jacobi Equation on Spaces of Constant Curvature

We review the theory of orthogonal separation of variables of the Hamilton-Jacobi equation on spaces of constant curvature, highlighting key contributions to the theory by Benenti. This theory