Speaker
Description
Semiclassical tunneling is usually formulated in Euclidean time, but for non-trivial initial states the appropriate Euclidean saddle and boundary conditions are not always obvious. I will introduce real-time path-integral approaches to tunneling, focusing on the steadyon construction based on complex semiclassical saddles, and use it to clarify how conserved quantities are incorporated.
I will first illustrate the steadyon construction with a quantum-mechanical particle tunneling at fixed angular momentum and energy. In this framework, tunneling is described directly in real time by complex semiclassical trajectories, with the initial-state energy and conserved charge encoded in the saddle-point boundary conditions. I will then show how, for the lowest-energy state in a fixed-charge sector, this real-time construction simplifies and can be mapped onto a purely Euclidean prescription, which can subsequently be generalized to field theory.
As a concrete application, I will discuss vacuum decay in a scalar theory with a conserved global $U(1)$ charge, starting from a homogeneous charged metastable state. Fixing the charge modifies the semiclassical problem already at the level of the saddle-point boundary conditions: the usual complex-field formulation involves twisted Euclidean boundary conditions and a complex saddle, but the problem can be recast as a real two-field Euclidean boundary-value problem that is suitable for numerical solution. At finite charge, the bounce departs from the usual $O(4)$-symmetric Coleman solution, the effective tunneling barrier is reduced, and the decay exponent decreases, leading to an enhancement of the decay rate. I will also discuss the real-time dynamics following nucleation, where charge redistribution around the expanding wall can lead to a subluminal terminal velocity even in vacuum, and finally comment on the generalization to finite temperature and finite chemical potential.