Goldstone bosons across thermal phase transitions

TL;DR

This paper investigates how Goldstone bosons behave across thermal phase transitions in quantum field theories, revealing their evolution from weakly to strongly damped states as temperature crosses the critical point.

Contribution

It explicitly characterizes the thermal evolution of Goldstone modes across phase transitions, highlighting their damping behavior in different phases.

Findings

Goldstone mode persists above critical temperature as a thermoparticle.

Weak damping in the broken phase, strong damping in the restored phase.

Thermal dissipation characterizes the phases and transition.

Abstract

Temperature has a significant effect on the properties of quantum field theories (QFTs) with a spontaneously broken symmetry, in particular on the massless Goldstone bosons that exist in the vacuum state. It has recently been shown using lattice calculations for a $\mathrm{U}(1)$ complex scalar field theory that the Goldstone mode persists even when the symmetry is restored above the critical temperature $T_{c}$, and has the properties of a screened excitation, a so-called thermoparticle. In this work, we continue the investigation of this theory by determining explicitly how the Goldstone mode evolves as the temperature is increased both below and above $T_{c}$. We find that the two phases of the theory are entirely characterised by the thermal dissipative effects experienced by the Goldstone mode, with the broken and symmetry-restored phases associated with weak and strong damping, respectively. These findings are consistent with the non-perturbative constraints imposed by spontaneous symmetry breaking, and provide a new way in which to characterise thermal phase transitions in QFTs.