Rindler Physics with a UV Cutoff on the Lattice

TL;DR

This paper studies a lattice quantum field theory in Rindler space with a UV cutoff, showing that the Unruh effect persists operationally but not exactly at the state level, and introduces a stretched horizon concept.

Contribution

It demonstrates how a UV cutoff affects the Rindler and Minkowski descriptions, revealing the persistence of the Unruh effect and a brick-wall-like horizon in a lattice setting.

Findings

Unruh effect remains operationally valid with a UV cutoff.

The Minkowski vacuum is not exactly thermal in the lattice Rindler Hamiltonian.

A stretched horizon replaces the UV singularity at the Rindler horizon.

Abstract

We investigate quantum field theory in Rindler space with a UV cutoff by considering a free scalar field on a lattice in Rindler coordinates. We find that the Minkowski vacuum is not exactly thermal with respect to the local lattice Rindler Hamiltonian. Nevertheless, for observables sufficiently far from the horizon, the Wightman function and the Unruh--DeWitt detector response reproduce the expected thermal behavior in the continuum limit. Thus, the Unruh effect survives operationally, even though exact thermality is lost at the state level. We also show that the Rindler vacuum energy density reproduces the standard continuum behavior away from the horizon, while the UV singularity at the horizon is replaced by a stretched-horizon contribution. Furthermore, the retarded Green function exhibits a component reflected at the stretched horizon, implying that an ingoing wave packet is reflected at a proper distance of order the cutoff. This provides an effective brick-wall picture in the UV-regulated theory. Our analysis suggests that, once a cutoff is introduced, the global Minkowski description and the wedge description based on a local Rindler Hamiltonian are no longer equivalent at the operator level.