Modular nuclearity: A generally covariant perspective

TL;DR

This paper introduces a modular l^p-condition for quantum field theories that extends nuclearity criteria to generally covariant settings, ensuring better state selection beyond free fields and flat spacetimes.

Contribution

It proposes a new covariant modular nuclearity condition applicable to a wide range of theories, extending previous Minkowski space results and analyzing its relation to Hadamard states.

Findings

The modular l^p-condition applies to all quasi-free Hadamard states.

It is stable under causal propagation and mixtures.

The condition is not equivalent to the Hadamard condition.

Abstract

A quantum field theory in its algebraic description may admit many irregular states. So far, selection criteria to distinguish physically reasonable states have been restricted to free fields (Hadamard condition) or to flat spacetimes (e.g. Buchholz-Wichmann nuclearity). We propose instead to use a modular l^p-condition, which is an extension of a strengthened modular nuclearity condition to generally covariant theories. The modular nuclearity condition was previously introduced in Minkowski space, where it played an important role in constructive two dimensional algebraic QFT's. We show that our generally covariant extension of this condition makes sense for a vast range of theories, and that it behaves well under causal propagation and taking mixtures. In addition we show that our modular l^p-condition holds for every quasi-free Hadamard state of a free scalar quantum field (regardless of mass or scalar curvature coupling). However, our condition is not equivalent to the Hadamard condition.