Vacuum decay in the Lorentzian path integral

Understand

We apply the Lorentzian path integral to the decay of a false vacuum and estimate the false-vacuum decay rate.

• To make the Lorentzian path integral convergent, the deformation of an integral contour is performed by following the Picard-Lefschetz theory.
• We show that the nucleation rate of a critical bubble, for which the corresponding bounce action is extremized, has the same exponent as the Euclidean approach.
• We also extend our computation to the nucleation of a bubble larger or smaller than the critical one to which the Euclidean formalism is not applicable.