Bubble nucleation to all orders

Abstract

This paper extends classical results by Langer and Kramers [1–3] and combines them with modern methods from high-temperature field theory [4–8]. Assuming Langevin dynamics, the end-product is an all-orders description of bubble-nucleation at high temperatures. Specifically, it is shown that equilibrium and non-equilibrium effects factorize to all orders — the nucleation rate splits into a statistical and a dynamical prefactor. The derivation clarifies, and incorporates, higher-order corrections from zero-modes [9–11]. The rate is also shown to be real to all orders in perturbation theory. The methods are applied to several models. As such, Feynman rules are given; the relevant power-counting is introduced; RG invariance is shown; the connection with the effective action is discussed, and an explicit construction of propagators in an inhomogeneous background is given. The formalism applies to both phase and Sphaleron transitions. While mainly focused on field theory, the methods are applicable to finite-dimensional systems. Finally, as this paper assumes an effective Langevin description [4–7, 12–14], all results only hold within this framework.