Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

Abstract

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a selfinteracting scalar field theory modeling the process of nucleation in four dimensional spacetime.This technique does not rely on the thin-wall approximation. The method is based on the GelfandYaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation.We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution. * Electronic address: dunne@phys.uconn.edu † Electronic address: hsmin@dirac.uos.ac.kr

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