BRST invariant approach to quantum mechanical tunneling

TL;DR

This paper introduces a BRST invariant method to address degeneracy issues in path integrals for quantum tunneling, avoiding Faddeev-Popov procedures and accurately calculating tunneling effects in the Sine-Gordon potential.

Contribution

A novel BRST invariant approach that simplifies the treatment of zero modes in quantum tunneling calculations without Faddeev-Popov procedures.

Findings

Accurately computes tunneling effects in the Sine-Gordon potential.

Results agree with traditional WKB calculations.

Provides a systematic way to handle zero modes in path integrals.

Abstract

A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path-integral calculationof quantum mechanical tunneling effects in which the problem arises due to the occurrence of zero modes. The Faddeev-Popov procedure is avoided and the integral over the zero mode is transformed in a systematic way into a well defined integral over instanton positions. No special procedure has to be adopted as in the Faddeev-Popov method in calculating the Jacobian of the transformation. The quantum mechanical tunneling for the Sine-Gordon potential is used as a test of the method and the width of the lowest energy band is obtained in exact agreement with that of WKB calculations.