A Goldstone Theorem in Thermal Relativistic Quantum Field Theory

TL;DR

This paper proves a Goldstone Theorem in thermal relativistic quantum field theory, linking spontaneous symmetry breaking to the decay rate of two-point functions, with implications for understanding massless excitations.

Contribution

It establishes a Goldstone Theorem in thermal QFT, connecting symmetry breaking to decay rates, a novel extension of the theorem to finite-temperature settings.

Findings

Decay rate matches that of massless free scalar fields

Spontaneous symmetry breaking relates to space-like decay of two-point functions

Open problems in thermal QFT are discussed

Abstract

We prove a Goldstone Theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of space-like decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed.