Transition state theory for the hyperbolic φ⁴ model

We study the expected transition frequency between the two metastable states of a stochastic wave equation with double-well potential. By transition state theory, the frequency factorizes into two components: one depends only on the invariant measure, given by the phi 4d quantum field theory, and the other takes the dynamics into account. We compute the first component with the variational approach to stochastic quantization when d = 2, 3. For the two-dimensional equation with random data but no stochastic forcing, we also compute the transmission coefficient leading to an Eyring-Kramers law.