On the Observer Dependence of the Quantum Effective Potential

TL;DR

This paper explores how the quantum effective potential depends on the observer's frame in an interacting field theory within Rindler space, revealing finite local potentials after renormalization and implications for symmetry restoration.

Contribution

It develops a formalism to compute the effective potential in Rindler space and analyzes observer-dependent effects on symmetry restoration in quantum field theory.

Findings

Effective potential is finite after renormalization in Rindler space.

Observer dependence affects symmetry restoration.

Formalism applies to interacting fields in curved spacetime.

Abstract

In this short paper, we investigate the consequences of observer dependence of the quantum effective potential for an interacting field theory. Specializing to $d+2$ dimensional Euclidean Rindler space, we develop the formalism to calculate the effective potential. While the free energy diverges due to the presence of the Rindler horizon, the effective potential, which is a local function of space, is finite after the necessary renormalization procedure. We apply the results of our formalism to understand the restoration of spontaneously broken $\mathbb{Z}_2$ symmetry in three and four dimensions.