Horizon temperature on the real line

TL;DR

This paper demonstrates an analogue of the Unruh effect for a quantum system on the real line, showing that a thermal distribution arises from the representation theory of affine transformations without relying on a metric or time.

Contribution

It introduces a novel derivation of the Unruh effect analogue using only affine group representations, independent of spacetime notions.

Findings

Thermal distribution emerges naturally in the model.

The derivation relies solely on affine transformation representations.

No notion of time or metric is required.

Abstract

We illustrate the analogue of the Unruh effect for a quantum system on the real line. Our derivation relies solely on basic elements of representation theory of the group of affine transformations without a notion of time or metric. Our result shows that a thermal distribution naturally emerges in connecting quantum states belonging to representations associated to distinct notions of translational symmetry.