Precision decay rate calculations in quantum field theory

This is the authors' abstract. We don't add key points for this paper.

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 semiclassical 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.