Vacuum decay in the Lorentzian path integral
  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.
