Tunneling — Quantum Restoration of Classically Broken Symmetries

Abstract

Quantum field theory combines the principles of quantum mechanics with the principles of special relativity and with the principles of causality and locality. Such a combination leads to an infinite number of degrees of freedom conveniently labeled e.g. by the points of space. The wave-function is replaced by a wave-functional supplying a probability amplitude for a field configuration. The last fifteen years brought about an understanding of quantum field theory in general and non-abelian gauge theories in particular that goes beyond the understanding gained through the application of simple perturbation theory. The most important achievement of this development is the so-called “standard model” of particle physics. As part of this development it was realized that there are tunneling phenomena in quantum field theory. It is thus not surprising that more than a decade ago a calculational scheme known as the “dilute instanton gas approximation” was developed by A.M. Polyakov and by G. t’Hooft to deal with tunneling phenomena 1.