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We investigate fermion production in the background of Minkowski spacesolutions to the equations of motion of $SU(2)$ gauge theory spontaneouslybroken via the Higgs mechanism. First, we attempt to evaluate the topologicalcharge $Q$ of the solutions. We find that for solutions $Q$ is not well-definedas an integral over all space-time. Solutions can profitably be characterizedby the (integer-valued) change in Higgs winding number $\Delta N_H$. We showthat solutions which dissipate at early and late times and which have nonzero$\Delta N_H$ must have at least the sphaleron energy. We show that if we couplea quantized massive chiral fermion to a classical background given by asolution, the number of fermions produced is $\Delta N_H$, and is not relatedto $Q$.Comment: Version to be published. Argument showing that the topological charge  of solutions is undefined has been strengthened and clarified. Conclusions  unchange

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