Vacuum tunneling and fluctuations around a most probable escape path

Abstract

We study vacuum tunneling in field theory directly in Minkowski space. We do this by extending the concept of "most probable escape path" (MPEP) first introduced by Banks, Bender, and Wu to the infinitedimensional configuration space of fields and then constructing a wave functional, satisfying a Schrödingertype equation, by a WKB expansion along this MPEP. The first-order results show that the tunneling process may indeed be described by one quantum variable tunneling in a one-dimensional potential barrier as proposed by us earlier for gauge theory. Corrections to this picture can now be calculated systematically. The first-higher-order corrections are shown to take the form of a "free energy" term that may be interpreted as a modification to the one-dimensional potential barrier obtained earlier.