Categorification of algebraic quantum field theories

Benini, Marco; Perin, Marco; Schenkel, Alexander; Woike, Lukas

Abstract

This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the 2-category of 2AQFTs. Examples of 2AQFTs that do not come from ordinary AQFTs via this embedding are constructed by a local gauging construction for finite groups, which admits a physical interpretation in terms of orbifold theories. A categorification of Fredenhagen’s universal algebra is developed and also computed for simple examples of 2AQFTs.

Citation

Benini, M., Perin, M., Schenkel, A., & Woike, L. (2021). Categorification of algebraic quantum field theories. Letters in Mathematical Physics, 111(2), Article 35. https://doi.org/10.1007/s11005-021-01371-8

• Journal Article Type: Article
• Acceptance Date: Feb 20, 2021
• Online Publication Date: Mar 16, 2021
• Publication Date: Mar 16, 2021
• Deposit Date: Mar 16, 2021
• Publicly Available Date: Mar 16, 2021
• Journal: Letters in Mathematical Physics
• Print ISSN: 0377-9017
• Electronic ISSN: 1573-0530
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 111
• Issue: 2
• Article Number: 35
• DOI: https://doi.org/10.1007/s11005-021-01371-8
• Keywords: Mathematical Physics; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/5397666
• Publisher URL: https://link.springer.com/article/10.1007/s11005-021-01371-8