On the prefactor in false vacuum decay

Abstract

This paper gives a survey of recent work in collaboration with G Dunne concerning a new method for computing determinants in quantum field-theoretic applications, using angular momentum cut-off regularization and renormalization. This method is generally applicable to the situation of computing the quantum fluctuations about a classical configuration that has a symmetry allowing the fluctuation operator to be radially separable. There are many such cases of interest in quantum field theory. Here I describe the case of the false vacuum decay rate in a self-interacting scalar field theory modelling the process of nucleation in a four-dimensional spacetime. The rate prefactor involves quantum fluctuations about the classical bounce solution, which is O(4) symmetric. The computational method is based on the Gelfand–Yaglom approach to determinants of ordinary differential operators, suitably extended to higher dimensions using angular momentum cut-off regularization. I also present a simple new formula for the zero-mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behaviour of the classical bounce solution.