Precision decay rate calculations in quantum field theory

TL;DR

This paper reviews the physical origin of tunneling in quantum field theory, discusses different calculation methods, and explores the sensitivity of universe lifetime to short-distance physics like quantum gravity.

Contribution

It provides a pedagogical review of tunneling rate calculations, compares traditional and recent methods, and highlights the impact of short-distance physics on universe stability.

Findings

Traditional and propagator-based tunneling methods compared

Insights into semi-classical solutions for tunneling

Sensitivity of universe lifetime to quantum gravity effects

Abstract

Tunneling in quantum field theory is worth understanding properly, not least because it controls the long term fate of our universe. There are however, a number of features of tunneling rate calculations which lack a desirable transparency, such as the necessity of analytic continuation, the appropriateness of using an effective instead of classical potential, and the sensitivity to short-distance physics. This paper attempts to review in pedagogical detail the physical origin of tunneling and its connection to the path integral. Both the traditional potential-deformation method and a recent more direct propagator-based method are discussed. Some new insights from using approximate semi-classical solutions are presented. In addition, we explore the sensitivity of the lifetime of our universe to short distance physics, such as quantum gravity, emphasizing a number of important subtleties.