Semiclassical Methods for Nonlinear Field Theories

Many modifications to the standard models of particle physics and cosmology lead to new forces. The effects of these so-called “fifth-forces” can be long range if the exchange particles that mediate them are light. Naturally, any viable fifth-force theory must account for its non-observation. One class of theories achieves this by introducing nonlinearities to the equations that describe the underlying fields, consequently screening them from local experiments. These nonlinearities present a challenge for characterising the quantum effects of fifth-force theories; even the question of whether the quantum corrections are relevant remains open for some. In this talk, I will discuss the saddlepoint approximation – a semiclassical method for computing leading order quantum corrections. I will demonstrate its effectiveness in the context of vacuum decay, and briefly discuss its relevance for fifth-force theories.