---
author:
- |
    [Detlev Buchholz$^a$  and   Stephen J. Summers$^b$ ]{}\
    ${}^a$ Institut für Theoretische Physik, Universität Göttingen,\
    37077 Göttingen, Germany\
    ${}^b$ Department of Mathematics, University of Florida,\
    Gainesville FL 32611, USA
date: Dedicated to Jacques Bros on the occasion of his seventieth birthday
title: 'Stable Quantum Systems in Anti–de Sitter Space: Causality, Independence and Spectral Properties'
---

Introduction and basic assumptions {#intro}
==================================

Quantum field theory in anti-de Sitter space–time (AdS) has been studied for almost 40 years (see [*e.g.*]{} [@F1; @AIS]), primarily because it was found that AdS occurs as the ground state geometry in certain supergravity theories with gauged internal symmetry [@BrFr; @dWNi2]. But it has become the object of an extraordinary amount of attention since the AdS-CFT correspondence has emerged.[^1] There is therefore motivation to clarify in a model–independent setting and in a mathematically rigorous manner the universal properties of such theories, as implied by generally accepted and physically meaningful assumptions. This investigation has lead us to results which apparently have not been remarked in any form in the literature before.

AdS is a maximally symmetric and globally static solution of the vacuum Einstein equations. We consider here AdS of any dimension $n \geq 2$, except 