Saddle-point approximation to the false vacuum decay at finite temperature in one-dimensional quantum mechanics

We calculate the false-vacuum decay rate in one-dimensional quantum mechanics on the basis of the saddle-point approximation in the Euclidean path integral at finite temperature. The saddle points are the finite-T and shifted bounce solutions, which are finite-period analogs of the (zero-temperature) bounce solution, and the shot solutions. We re-examined the zero-temperature result by Callan and Coleman and compare with the zero-temperature limit of our results. We also perform some numerical calculations to illustrate the temperature dependence of the decay rate and compare it with the result by Affleck.