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

TL;DR

This paper explores exact solutions in classical gauge theories within even-dimensional spacetimes, analyzing properties in dimensions 2, 4, and 6, and proposing a consistent formulation for D=6 with point particles.

Contribution

It introduces a new formulation of classical gauge theories in six dimensions, including a particle Lagrangian dependent on acceleration and detailed analysis of radiation and self-interaction.

Findings

Radiation is absent in D=2, making processes reversible.

In D=6, radiation rate and particle equations of motion are derived.

Non-Abelian solutions are absent except in D=4, where Coulomb-like solutions exist.

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.