Modular nuclearity: A generally covariant perspective

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.

42 pages

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Cited by in corpus (7)

• An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes
• On separable states in relativistic quantum field theory
• Relative entanglement entropy for widely separated regions in curved spacetime
• Locally covariant quantum field theory and the spin-statistics connection
• Curving Flat Space-Time by Deformation Quantization?
• Modular Nuclearity and Entanglement measures
• Relative entanglement entropy of thermal states of Klein-Gordon and Dirac quantum field theories