Exact Solutions of Classical Electrodynamics and the Yang--Mills--Wong Theory in Even-Dimensional Spacetime

Abstract

Exact solutions of classical gauge theories in even-dimensional (D=2n) spacetimes are discussed. Common and specific properties of these solutions are analyzed for the particular dimensions D=2, D=4, and D=6. A consistent formulation of classical gauge field theories with pointlike charged or colored particles is proposed for D=6. The particle Lagrangian must then depend on the acceleration. The self-interaction of a point particle is considered for D=2 and D=6. In D=2, radiation is absent and all processes are reversible. In D=6, the expression for the radiation rate and the equation of motion of a self-interacting particle are derived; from which follows that the Zitterbewegung always leads to radiation. It is shown that non-Abelian solutions are absent for any D not equal to 4; only Coulomb-like solutions, which correspond to the Abelian limit of the D-dimensional Yang--Mills--Wong theory, are admitted.