The scaling limits of KMS states on the Rindler horizon

TL;DR

This paper develops a new framework for analyzing the scaling limits of quantum states at boundaries, specifically characterizing L1-KMS states on the Rindler wedge and computing the scaling limit of the KMS state on the Rindler horizon.

Contribution

It introduces a novel boundary scaling framework and fully characterizes L1-KMS states on the Rindler wedge, correcting previous inaccuracies in the scaling limit analysis.

Findings

Rigorous computation of the scaling limit of the KMS state on the Rindler horizon.

Introduction of a new boundary scaling framework for distributions.

Correction of previous results regarding KMS states at the Rindler horizon.

Abstract

The standard concept of scaling limits of distributions on manifolds is reformulated, and then a new framework for scaling at boundary points is provided. Next, we introduce a class of so-called L1 - KMS states, which is subsequently fully characterized for the Rindler wedge. Using these tools, we compute rigorously the scaling limit of the regular KMS state of the free scalar quantum field on the Rindler horizon. Thereby, we correct certain inaccurate results of founding paper [1], nevertheless fully corroborating the physical essence of them.