Unruh effect universality: emergent conical geometry from density operator

TL;DR

This paper demonstrates the universality of the Unruh effect across different quantum fields by deriving quantum corrections via the density operator, linking thermodynamics with emergent conical geometries.

Contribution

It introduces a statistical approach to substantiate the Unruh effect's universality and shows how conical geometries emerge from thermodynamic considerations.

Findings

Quantum corrections support the Unruh effect's universality.

Infrared divergences are regularized for scalar fields.

Results match those from conical space calculations.

Abstract

The Unruh effect has been investigated from the point of view of the quantum statistical Zubarev density operator in space with the Minkowski metric. Quantum corrections of the fourth order in acceleration to the energy-momentum tensor of real and complex scalar fields, and Dirac field are calculated. Both massless and massive fields are considered. The method for regularization of discovered infrared divergences for scalar fields is proposed. The calculated corrections make it possible to substantiate the Unruh effect from the point of view of the statistical approach, and to explicitly show its universality for various quantum field theories of massless and massive fields. The obtained results exactly coincide with the ones obtained earlier by calculation of the vacuum average of energy-momentum tensor in a space with a conical singularity. Thus, the duality of two methods for describing an accelerated medium is substantiated. One may also speak about the emergence of geometry with conical singularity from thermodynamics. In particular, the polynomiality of the energy-momentum tensor and the absence of higher-order corrections in acceleration can be explicitly demonstrated.