Functional methods for false vacuum decay in real time

Understand

We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections.

• For this purpose, we use the well-known fact that Euclidean saddle points in terms of real fields can be analytically continued to complex saddles of the action in Minkowski space.
• We also use Picard-Lefschetz theory in order to determine the middle-dimensional steepest-descent surface in the complex field space, constructed from Lefschetz thimbles, on which the path integral is to be performed.
• As an alternative to extracting the decay rate from the imaginary part of the ground-state energy of the false vacuum, we use the optical theorem in order to derive it from the real-time amplitude for forward scattering.