Revisiting Vacuum decay in Field Theory

TL;DR

This paper refines the quantum field theory tunneling formalism by using generalized WKB methods, addressing previous issues, and discusses implications for the stability of the standard model vacuum.

Contribution

It introduces a wave packet approach to tunneling in quantum field theory and clarifies the application to the standard model vacuum stability.

Findings

Differences in pre-factor compared to Coleman's approach.

Wave packet formulation for time evolution.

Implications for standard model vacuum stability.

Abstract

We revisit the formalism for tunneling in quantum field theory developed by Coleman and collaborators. In particular using the generalization of WKB methods for tunneling in quantum mechanics we avoid the problems with negative eigenvalues and convexity issues associated with Coleman's approach. While the exponential factor is the same, we find differences in the pre-factor. Then we point out that to actually discuss the time evolution of the state, we need a wave packet formulation which we proceed to discuss. Next we address the problem of justifying the application of semi-classical tunneling calculations to the decay of the standard model vacuum, where the classical potential signifies absolute stability, though the effective potential appears to imply the possibility of meta-stability (with more than one local minimum). This is in contrast to the usual situation in applications of the formalism for tunneling, where the \textit{classical} potential has more than one local minimum.