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

Abstract

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 $Q$.

Version to be published. Argument showing that the topological charge of solutions is undefined has been strengthened and clarified. Conclusions unchanged

References in corpus (3)

• Spherical Shells of Classical Gauge Field and their Topological Charge as a Perturbative Expansion
• Anomalies without Massless Particles
• Gradient Approach to the Sphaleron Barrier

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