  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.
