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Open AccessArticle

Modular Nuclearity: A Generally Covariant Perspective

1
School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
2
Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, Leipzig 04103, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Palle E.T. Jorgensen
Received: 5 December 2015 / Revised: 18 January 2016 / Accepted: 25 January 2016 / Published: 29 January 2016
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 ℓp -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 ℓp -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. View Full-Text
Keywords: modular theory; nuclear maps; quantum field theory; general covariance modular theory; nuclear maps; quantum field theory; general covariance
MDPI and ACS Style

Lechner, G.; Sanders, K. Modular Nuclearity: A Generally Covariant Perspective. Axioms 2016, 5, 5.

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