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Operads for algebraic quantum field theory

Benini, Marco; Schenkel, Alexander; Woike, Lukas


Marco Benini

Lukas Woike


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.


Benini, M., Schenkel, A., & Woike, L. (2020). Operads for algebraic quantum field theory. Communications in Contemporary Mathematics, 2050007.

Journal Article Type Article
Acceptance Date Dec 18, 2019
Online Publication Date Mar 2, 2020
Publication Date Mar 2, 2020
Deposit Date Jan 3, 2020
Publicly Available Date Mar 3, 2021
Journal Communications in Contemporary Mathematics
Print ISSN 0219-1997
Electronic ISSN 1793-6683
Publisher World Scientific
Peer Reviewed Peer Reviewed
Pages 2050007
Keywords Mathematical Physics; High Energy Physics - Theory; Category Theory;
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