BRST-invariant approach to quantum mechanical tunneling

A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path-integral calculation of 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.