Solutions of classical gauge field theories with spin and internal symmetry

Abstract

We examine finite-dimensional matrix solutions to the equations of classical gauge field theories and interpret them in terms of solitons with spin and internal symmetry. The equations are reduced to relations among scalar quantities which turn out to be the same as those obtained for spinless solitons with no internal degrees of freedom, both for spherically symmetric and cylindrically symmetric situations. General formulas are derived for the invariant magnetic field associated with the theory. In the spherical case with degrees of freedom corresponding to spin 1 2 and isospin 1 2 we find that the solitons are monopoles with magnetic charge satisfying the quantization condition eg = 1 2 . Finally, we discuss the difficulties associated with our interpretation.