Quantum field nucleating and Wigner functions

We present a novel real-time framework for the decay of metastable states in quantum field theories using Wigner functions. The framework introduces a nonperturbative nucleation rate formula that captures both quantum tunneling and over-the-barrier nucleation, alongside steps to evaluate it perturbatively. We apply it to a simple thermal example with direct relevance to current analog experiments. Our derived one-loop nucleation rate fundamentally differs from the widely cited high-temperature result by Linde: The prefactor contains quantum effects and also asymptotes to a differing form at high temperatures, where the quantum effects become negligible. Rather, the result is a generalization of Affleck's rate formula to quantum field theories, asymptoting to the effective field theory approach, and Langer's rate, at high temperatures. The example also reveals that the high-temperature side of the ``quantum-to-classical'' transition of thermal vacuum decay is still inherently quantum mechanical, even though the bounce background possesses the classical, $\mathrm{O}(d)\times S^1$, symmetry.