Smooth 1-Dimensional Algebraic Quantum Field Theories

Benini, Marco; Perin, Marco; Schenkel, Alexander

Abstract

This paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using stacks of categories, this proposal is realized concretely for the simplest case of 1-dimensional spacetimes, leading to a stack of smooth 1-dimensional AQFTs. Concrete examples of smooth AQFTs, of smooth families of smooth AQFTs and of equivariant smooth AQFTs are constructed. The main open problems that arise in upgrading this approach to higher dimensions and gauge theories are identified and discussed.

Citation

Benini, M., Perin, M., & Schenkel, A. (2022). Smooth 1-Dimensional Algebraic Quantum Field Theories. Annales Henri Poincaré, 23, 2069-2111. https://doi.org/10.1007/s00023-021-01132-2

• Journal Article Type: Article
• Acceptance Date: Oct 25, 2021
• Online Publication Date: Dec 13, 2021
• Publication Date: 2022-06
• Deposit Date: Dec 10, 2021
• Publicly Available Date: Dec 13, 2021
• Journal: Annales Henri Poincaré
• Print ISSN: 1424-0637
• Electronic ISSN: 1424-0661
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Pages: 2069-2111
• DOI: https://doi.org/10.1007/s00023-021-01132-2
• Keywords: algebraic quantum field theory; stacks of categories; vertical geometry of fiber bun- dles; smoothly parametrized differential equations MSC 2020: 81Txx; 18F20; 18N10
• Public URL: https://nottingham-repository.worktribe.com/output/6916130
• Publisher URL: https://link.springer.com/article/10.1007/s00023-021-01132-2