Modular Nuclearity: A Generally Covariant Perspective

Axioms

Ko Sanders¹  Gandalf Lechner² 

[1] Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, Leipzig 04103, Germany;School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK;

关键词: modular theory;    nuclear maps;    quantum field theory;    general covariance;   

DOI  :  10.3390/axioms5010005

来源: DOAJ

【 摘 要 】

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 modularℓp -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 modularℓp -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.

【 授权许可】

Unknown