# 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} }

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…

## 10 Citations

### 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

- MathematicsJournal 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

- MathematicsUniverse
- 2022

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

- Physics
- 2022

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…

### Harmonic oscillator coherent states from the orbit theory standpoint

- Mathematics, Physics
- 2022

We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial diﬀerential equations. The…

### Gravitational Waves of Type III Shapovalov Spacetimes: Particle Trajectories, Geodesic Deviation and Tidal Accelerations

- Physics
- 2022

For gravitational-wave spacetimes of Shapovalov type III, exact general solutions of geodesic deviation equations and equations of motion of test particles are obtained. Solutions are found in a…

### Type I Shapovalov wave spacetimes in the Brans-Dicke scalar-tensor theory of gravity

- Physics
- 2022

: Exact solutions for Shapovalov wave spacetimes of type I in the scalar-tensor theory of gravity of Brans-Dicke are constructed. Shapovalov’s wave spacetimes describe gravitational-wave models that…

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

- MathematicsSymmetry
- 2022

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

- PhysicsThe European Physical Journal C
- 2022

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…

### Maxwell equations in homogeneous spaces with solvable groups of motions

- Mathematics
- 2022

A special place in mathematical physics is occupied by the problem of exact integration of the field equations for electromagnetic and gravitational fields. The problem can be successful solved if…

### Geodesic deviation and tidal acceleration in the gravitational wave of the Bianchi type IV universe

- PhysicsThe European Physical Journal Plus
- 2022

## 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

- MathematicsJournal 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

- Mathematics
- 2021

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

- Mathematics
- 2012

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)

- Mathematics
- 2020

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

- Mathematics
- 2019

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

- MathematicsSymmetry
- 2020

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

- MathematicsSymmetry
- 2021

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

- Mathematics
- 2020

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)

- MathematicsSymmetry
- 2020

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

- Mathematics
- 2016

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…