Precision decay rate calculations in quantum field theory

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.