On the Metastability of Quantum Fields in Thermal Bath

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.