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

Fate of False Vacuum in Non-perturbative Regimes