Homotopy theory of algebraic quantum field theories

Benini, Marco; Schenkel, Alexander; Woike, Lukas

Abstract

Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical model structure and explain the important conceptual and also practical consequences of this result. As a concrete application we provide a derived version of Fredenhagen’s universal algebra construction, which is relevant e.g. for the BRST/BV formalism. We further develop a homotopy theoretical generalization of algebraic quantum field theory with a particular focus on the homotopy-coherent Einstein causality axiom. We provide examples of such homotopy-coherent theories via (1) smooth normalized cochain algebras on ∞-stacks, and (2) fiber-wise groupoid cohomology of a category fibered in groupoids with coefficients in a strict quantum field theory.

Citation

Benini, M., Schenkel, A., & Woike, L. (2019). Homotopy theory of algebraic quantum field theories. Letters in Mathematical Physics, 109(7), 1487-1532. https://doi.org/10.1007/s11005-018-01151-x

• Journal Article Type: Article
• Acceptance Date: Dec 22, 2018
• Online Publication Date: Jan 16, 2019
• Publication Date: 2019-07
• Deposit Date: Jan 11, 2019
• Publicly Available Date: Jan 17, 2019
• Journal: Letters in Mathematical Physics
• Print ISSN: 0377-9017
• Electronic ISSN: 1573-0530
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 109
• Issue: 7
• Pages: 1487-1532
• DOI: https://doi.org/10.1007/s11005-018-01151-x
• Keywords: Mathematical Physics; High Energy Physics - Theory; Algebraic Topology
• Public URL: https://nottingham-repository.worktribe.com/output/1464279
• Publisher URL: https://link.springer.com/article/10.1007/s11005-018-01151-x