Fermion Production in the Background of Minkowski Space Classical Solutions in Spontaneously Broken Gauge Theory

E. Farhi, J. Goldstone, S. Gutmann, K. Rajagopal, R. Singleton

Published 1994-10-25, updated 1995-02-03Version 2

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 Higgs winding number $\Delta N_H$. We show that 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 couple a quantized massive chiral fermion to a classical background given by a solution, the number of fermions produced is $\Delta N_H$, and is not related to $Q$.