Spherical Shells of Classical Gauge Field and their Topological Charge as a Perturbative Expansion

Abstract

We consider the classical equations of motion of $SU(2)$ gauge theory, without a Higgs field, in Minkowski space. We work in the spherical ansatz and develop a perturbative expansion in the coupling constant $g$ for solutions which in the far past look like freely propagating spherical shells. The topological charge $Q$ of these solutions is typically non-integer. We then show that $Q$ can be expressed as a power series expansion in $g$ which can be nonzero at finite order. We give an explicit analytic calculation of the order $g^5$ contribution to $Q$ for specific initial pulses. We discuss the relation between our findings and anomalous fermion number violation, and speculate on the physical implications of our results.

18 pages in REVTEX

References in corpus (1)

• Minkowski Space Non-Abelian Classical Solutions with Non-Integer Winding Number Change

Cited by in corpus (6)

• Fermion Production in the Background of Minkowski Space Classical Solutions in Spontaneously Broken Gauge Theory
• Sphalerons and Conformally Compactified Minkowski Spacetime
• Gauge Invariant Variables for Spontaneously Broken SU(2) Gauge Theory in the Spherical Ansatz
• Fermion Number Violation in the Background of a Gauge Field in Minkowski Space
• Anomalous Violation of Conservation Laws in Minkowski Space
• Gribov copies and topological charge