Passive States for Essential Observers

TL;DR

This paper unifies and extends results on passive states for essential observers, showing invariance, thermal properties, and structural features of such states in quantum field theory across various spacetime models.

Contribution

It provides a unified framework for passive states, including new models like higher-dimensional Minkowski space, and details their invariance, thermal nature, and modular properties.

Findings

States are invariant under isometry groups.

States are KMS at a temperature determined by Lie algebra constants.

A variant of the Reeh-Schlieder property holds for these states.

Abstract

The aim of this note is to present a unified approach to the results given in \cite{bb99} and \cite{bs04} which also covers examples of models not presented in these two papers (e.g. $d$-dimensional Minkowski space-time for $d\geq 3$). Assuming that a state is passive for an observer travelling along certain (essential) worldlines, we show that this state is invariant under the isometry group, is a KMS-state for the observer at a temperature uniquely determined by the structure constants of the Lie algebra involved and fulfills (a variant of) the Reeh-Schlieder property. Also the modular objects associated to such a state and the observable algebra of an observer are computed and a version of weak locality is examined.