Fate of False Vacuum in Non-perturbative Regimes

TL;DR

This paper develops a non-perturbative formalism for analyzing false vacuum decay in scalar field theories, incorporating exact Green's functions and elliptical functions to improve understanding beyond weak coupling regimes.

Contribution

It introduces a simple non-perturbative approach using exact Green's functions and elliptical functions to analyze false vacuum decay, extending results beyond perturbative limits.

Findings

Effective potential with false minimum at origin

Derived analytic formulas for decay rate

Reproduces perturbative results at weak coupling

Abstract

We use some exact results in the scalar field theory to revise the analysis by Coleman and Callan about the false vacuum decay and propose a simple non-perturbative formalism. We introduce exact Green's function which incorporates non-perturbative corrections in the strong coupling regimes of the theory. The solution of the scalar field theory involves Jacobi elliptical function and has been used to calculate the effective potential for any arbitrary coupling values. We demonstrate the use of this formalism in a simple $\lambda \phi^4$ theory and show that the effective potential exhibits a false minimum at the origin. We then calculate the false vacuum decay rate and suggest simple analytic formulas which may be useful for the analysis for the first order phase transition beyond the perturbative regime. In our methodology, we show that the standard results obtained in perturbation theory are reproduced by taking the coupling values very small.