Significance of zero modes in path--integral quantization of solitonic theories with BRST invariance

TL;DR

This paper explores the crucial role of zero modes in the path-integral quantization of solitonic theories, demonstrating a BRST invariant approach to obtain well-defined transition amplitudes in a Skyrme-like model.

Contribution

It introduces a novel method for quantizing solitonic models that avoids explicit time dependence, maintaining BRST invariance and applicability in the one-loop approximation.

Findings

Successful quantization of a Skyrme-like model with topological vortices.

Development of an alternative quantization method without time dependence.

Establishment of a well-defined transition amplitude in the one-loop approximation.

Abstract

The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1+2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to - the one-loop approximation.