Path-integral formula for local thermal equilibrium

TL;DR

This paper develops a path-integral approach for relativistic quantum fields in local thermal equilibrium, revealing emergent curved spacetime and symmetries, and identifies a thermodynamic potential as a generating functional for conserved currents.

Contribution

It introduces a comprehensive path-integral formulation that captures the emergence of thermal spacetime and its symmetries in relativistic quantum fields.

Findings

Emergence of thermally induced curved spacetime with full diffeomorphism invariance.

Identification of the Masseiu-Planck functional as a generating functional for conserved currents.

Discovery of symmetry properties like Kaluza-Klein gauge symmetry and spatial diffeomorphism symmetry.

Abstract

We develop a complete path-integral formulation of relativistic quantum fields in local thermal equilibrium, which brings about the emergence of thermally induced curved spacetime. The resulting action is shown to have full diffeomorphism invariance and gauge invariance in thermal spacetime with imaginary-time independent backgrounds. This leads to the notable symmetry properties of emergent thermal spacetime: Kaluza-Klein gauge symmetry, spatial diffeomorphism symmetry, and gauge symmetry. A thermodynamic potential in local thermal equilibrium, or the so-called Masseiu-Planck functional, is identified as a generating functional for conserved currents such as the energy-momentum tensor and the electric current.