SO(4) Reduction of the SU(N) Yang–Mills–Dirac equations

Abstract

The equations in compactified Minkowski space that describe SU(N) Yang–Mills fields minimally coupled to Dirac spinor fields transforming under the lowest-dimensional representation(s) of SU(N) are reduced by the action of an SO(4) subgroup of the conformal group of space-time. The reduced systems can be interpreted as Hamiltonian systems with symmetry constrained by a condition on the associated moment maps.