Marco Benini
Operads for algebraic quantum field theory
Benini, Marco; Schenkel, Alexander; Woike, Lukas
Abstract
We construct a colored operad whose category of algebras is the category of algebraic quantum field theories. This is achieved by a construction that depends on the choice of a category, whose objects provide the operad colors, equipped with an additional structure that we call an orthogonality relation. This allows us to describe different types of quantum field theories, including theories on a fixed Lorentzian manifold, locally covariant theories and also chiral conformal and Euclidean theories. Moreover, because the colored operad depends functorially on the orthogonal category, we obtain adjunctions between categories of different types of quantum field theories. These include novel and interesting constructions such as time-slicification and local-To-global extensions of quantum field theories. We compare the latter to Fredenhagen's universal algebra.
Citation
Benini, M., Schenkel, A., & Woike, L. (2021). Operads for algebraic quantum field theory. Communications in Contemporary Mathematics, 23(2), Article 2050007. https://doi.org/10.1142/S0219199720500078
Journal Article Type | Article |
---|---|
Acceptance Date | Dec 18, 2019 |
Online Publication Date | Mar 2, 2020 |
Publication Date | Mar 1, 2021 |
Deposit Date | Jan 3, 2020 |
Publicly Available Date | Mar 29, 2024 |
Journal | Communications in Contemporary Mathematics |
Print ISSN | 0219-1997 |
Electronic ISSN | 1793-6683 |
Publisher | World Scientific |
Peer Reviewed | Peer Reviewed |
Volume | 23 |
Issue | 2 |
Article Number | 2050007 |
DOI | https://doi.org/10.1142/S0219199720500078 |
Keywords | Mathematical Physics; High Energy Physics - Theory; Category Theory; |
Public URL | https://nottingham-repository.worktribe.com/output/2460446 |
Publisher URL | https://www.worldscientific.com/doi/10.1142/S0219199720500078 |
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