Lagrangian Becchi-Rouet-Stora-Tyutin treatment of collective coordinates

TL;DR

This paper develops a BRST-based Lagrangian approach to quantize collective coordinates in systems with broken non-abelian symmetries, demonstrating gauge independence of the partition function up to two loops.

Contribution

It introduces a BRST antifield formalism for quantizing collective coordinates in Lagrangian systems with non-abelian symmetry breaking.

Findings

Partition function computed perturbatively to two loops

Results are gauge-fixing parameter independent

Applicable to particles in Riemannian manifolds with broken symmetries

Abstract

The Becchi-Rouet-Stora-Tyutin (BRST) treatment for the quantization of collective coordinates is considered in the Lagrangian formalism. The motion of a particle in a Riemannian manifold is studied in the case when the classical solutions break a non-abelian global invariance of the action. Collective coordinates are introduced, and the resulting gauge theory is quantized in the BRST antifield formalism. The partition function is computed perturbatively to two-loops, and it is shown that the results are independent of gauge-fixing parameters.