Next Article in Journal
Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process
Next Article in Special Issue
Infinite-dimensional Lie Algebras, Representations, Hermitian Duality and the Operators of Stochastic Calculus
Previous Article in Journal
Data Farming Process and Initial Network Analysis Capabilities
Article Menu

Export Article

Open AccessArticle
Axioms 2016, 5(1), 5; doi:10.3390/axioms5010005

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
View Full-Text   |   Download PDF [431 KB, uploaded 29 January 2016]

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 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top