Thermal Activation Rates in the Chirally Asymmetric Gross-Neveu Model

Abstract

We address the problem of how to incorporate quantum effects into the calculation of finite-temperature decay rates for a metastable state of a quantum field theory. To do this, we consider the Gross-Neveu model with an explicit chiral symmetry breaking term, which allows for a metastable state. This theory can be shown to have a "critical bubble" which is a solution to the *exact* equations of motions (i.e. to all orders in perturbation theory, including all higher derivative, quantum and thermal corrections). This configuration mediates the thermal activation of the metastable vacuum to the true ground state, with a decay rate $Γ\propto \exp(-F_c/T)$, where $F_c$ is the free energy of the critical bubble. We then compare this exact calculation to various approximations that have been used in previous work. We find that these approximations all *overestimate* the activation rate. Furthermore, we study the effect of finite baryon number upon the bubble profile and the activation barriers. We find that beyond a critical baryon number the activation barriers disappear altogether.