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Operads for algebraic quantum field theory

Marco Benini

Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg 20146, Germany

E-mail Address: [email protected]

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Alexander Schenkel

School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK

E-mail Address: [email protected]

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, and

Lukas Woike

Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg 20146, Germany

E-mail Address: [email protected]

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https://doi.org/10.1142/S0219199720500078Cited by:15 (Source: Crossref)

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.

Keywords:

AMSC: 81Txx, 18D50

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