Exact solutions of classical electrodynamics and the Yang-Mills-Wong theory in even-dimensional space-time (Q1567852)

The author discusses properties of exact solutions of classical gauge theories in the space-time of even dimension \(D\) and their dependence on \(D\). For \(D=6\), he proposes a consistent formulation of classical gauge theory with pointlike charged or colored particles such that the particle Lagrangian depends on acceleration. The equation of motion of a self-interacting particle is given. It is shown that a free particle may tremble, and the trembling always leads to radiation. For \(D=2\), the radiation is absent and all processes are invertible with respect to time. The author shows also that non-abelian solutions in the theory of Yang-Mills-Wong exist only in dimension \(D=4\).