Strictification theorems for the homotopy time-slice axiom

Benini, Marco; Carmona, Victor; Schenkel, Alexander

Abstract

It is proven that the homotopy time-slice axiom for many types of algebraic quantum field theories (AQFTs) taking values in chain complexes can be strictified. This includes the cases of Haag–Kastler-type AQFTs on a fixed globally hyperbolic Lorentzian manifold (with or without time-like boundary), locally covariant conformal AQFTs in two spacetime dimensions, locally covariant AQFTs in one spacetime dimension, and the relative Cauchy evolution. The strictification theorems established in this paper prove that, under suitable hypotheses that hold true for the examples listed above, there exists a Quillen equivalence between the model category of AQFTs satisfying the homotopy time-slice axiom and the model category of AQFTs satisfying the usual strict time-slice axiom.

Citation

Benini, M., Carmona, V., & Schenkel, A. (2023). Strictification theorems for the homotopy time-slice axiom. Letters in Mathematical Physics, 113(1), Article 20. https://doi.org/10.1007/s11005-023-01647-1

• Journal Article Type: Article
• Acceptance Date: Jan 31, 2023
• Online Publication Date: Feb 13, 2023
• Publication Date: Feb 13, 2023
• Deposit Date: Feb 14, 2023
• Publicly Available Date: Feb 22, 2023
• Journal: Letters in Mathematical Physics
• Print ISSN: 0377-9017
• Electronic ISSN: 1573-0530
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 113
• Issue: 1
• Article Number: 20
• DOI: https://doi.org/10.1007/s11005-023-01647-1
• Keywords: Article, Algebraic quantum field theory, Gauge theory, Homotopical algebra, Chain complexes, Operads, Localizations, 81T05, 81T70, 18N40, 18N55
• Public URL: https://nottingham-repository.worktribe.com/output/17377591
• Publisher URL: https://link.springer.com/article/10.1007/s11005-023-01647-1