Temperatures of renormalizable quantum field theories in curved spacetime

TL;DR

This paper derives a generalized temperature formula for an Unruh-DeWitt detector in curved spacetime, incorporating acceleration, spacetime curvature, and quantum field polarization, with implications for thermal equilibrium conditions.

Contribution

It provides a new expression for temperature in curved spacetime for renormalizable quantum fields, including a constraint on quantum polarization in thermal equilibrium.

Findings

Temperature depends on acceleration, curvature, and polarization.

Derived a constraint on quantum polarization in thermal equilibrium.

Generalized temperature formula for conformally invariant fields.

Abstract

In this paper we compute the temperature registered by an Unruh-DeWitt detector coupled to a Hadamard renormalizable quantum field in an arbitrary state, moving along an accelerated trajectory in a curved spacetime. For a massless and conformally invariant field, the generalized expression for the temperature is given by the quadratic sum of the 4-acceleration, Raychaudhuri scalar, and renormalized field polarization. We can further find a novel constraint on the renormalized quantum field polarization in relativistic systems that are in global thermal equilibrium.