On the Metastability of Quantum Fields in Thermal Bath

Abstract

We investigate the metastability of scalar fields in quantum field theories at finite temperature, focusing on a detailed understanding of the bounce solution. At finite temperature, the bounce solution depends on two variables: the Euclidean time $τ$ and the spatial radial distance $r$, and it is periodic in the $τ$ direction. We propose a novel method to determine the bounce that describes transitions in a thermal bath, suitable for numerical calculations. Two types of bounces exist for transitions in the thermal bath: $τ$-dependent and $τ$-independent bounces. We apply our method to compute these bounces in several models, including both thin-wall and thick-wall scenarios, to examine their properties. Specifically, we evaluate the critical temperature below which the $τ$-independent bounce becomes destabilized due to fluctuations, rendering it irrelevant. We demonstrate that in the thick-wall case, the $τ$-dependent bounce smoothly transitions into the $τ$-independent one as temperature increases, whereas in the thin-wall case, the transition between the two types of bounces is discontinuous.