Exact solutions of classical electrodynamics and the Yang-Mills-Wong theory in even-dimensional space-time

Exact solutions of classical gauge theories in even-dimensional (D=2n) space-time are discussed. Common and specific properties of these solutions are analyzed for the particular dimensions D=2, D=4, and D=6. The 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. In D=2, radiation is absent and all processes are invertible w.r.t. time. In D=6, the expression for the radiation intensity, as well as the equation of motion of a self-interacting particle, is obtained; trembling always leads to radiation. Non-Abelian solutions are absent for any D≠4, and only Coulomb-like solutions, which correspond to the Abelian limit of the D-dimensional Yang-Mills-Wong theory, are admitted. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 119–135, April, 1999.