Fermion production in the background of Minkowski space classical solutions in spontaneously broken gauge theory

We investigate fermion production in the background of Minkowski space solutions to the equations of motion of SU(2) gauge theory spontaneously broken via the Higgs mechanism. First, we attempt to evaluate the topological charge Q of the solutions. We find that for solutions Q is not well defined as an integral over all space-time. Solutions can profitably be characterized by the (integer-valued) change in the Higgs winding number Δ${\mathit{N}}_{\mathit{H}}$. We show that solutions which dissipate at early and late times and which have a nonzero Δ${\mathit{N}}_{\mathit{H}}$ must have at least the sphaleron energy. We show that if we couple a quantized massive chiral fermion to a classical background given by a solution, the number of fermions produced is Δ${\mathit{N}}_{\mathit{H}}$, and is not related to Q.