Maxwell’s Equations in Homogeneous Spaces for Admissible Electromagnetic Fields

Abstract

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 symmetry operators (integrals of motion) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell’s equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solutions depend on six arbitrary time functions, so it is possible to use them to integrate field equations in the theory of gravity.

Keywords

• Maxwell’s vacuum equations
• Hamilton–Jacobi equation
• Klein–Gordon–Fock equation
• algebra of symmetry operators
• separation of variables
• linear partial differential equations