Becchi-Rouet-Stora-Tyutin quantization of a soliton model in 2+1 dimensions

TL;DR

This paper applies the BRST quantization method to solitons in a 2+1 dimensional non-linear $O(3)$ model, providing a systematic approach to zero-modes and calculating two-loop corrections to soliton mass.

Contribution

It introduces a systematic BRST quantization framework for solitons in a 2+1D non-linear model, handling zero-modes and residual interactions.

Findings

Derived the BRST Hamiltonian for the model.

Showed residual interactions are perturbatively IR-divergence-free.

Computed the two-loop correction to the soliton mass.

Abstract

The Becchi-Rouet-Stora-Tyutin (BRST) method is applied to the quantization of the solitons of the non-linear $O(3)$ model in $2+1$ dimensions. We show that this method allows for a simple and systematic treatment of zero-modes with a non-commuting algebra. We obtain the expression of the BRST hamiltonian and show that the residual interaction can be perturbatively treated in an IR-divergence-free way. As an application of the formalism we explicitly evaluate the two-loop correction to the soliton mass.