Semiclassical probability distribution function for finite-temperature field theory

Abstract

We study semiclassical methods for evaluating the canonical probability distribution function $\rho \left(\phi \right)=〈\phi \left|\exp \right(-\beta H\left)\right|\phi 〉$ in field theory for systems in thermodynamic equilibrium. Field configurations which dominate the semiclassical distribution function are interpretable as "finite-temperature most-probable escape paths" (FTMPEP's) in field space and are related to the recently discovered caloron solutions, which are known to partially dominate the semiclassical partition function $Z=\int D\phi \rho \left(\phi \right)$. We present a semiclassical path-integral approximation for the distribution function and also discuss a Hartree self-consistent field approximation.