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Homotopy theory of algebraic quantum field theories

Benini, Marco; Schenkel, Alexander; Woike, Lukas


Marco Benini

Lukas Woike


Motivated by gauge theory, we develop a general framework for chain complex valued algebraic quantum field theories. Building upon our recent operadic approach to this subject, we show that the category of such theories carries a canonical model structure and explain the important conceptual and also practical consequences of this result. As a concrete application we provide a derived version of Fredenhagen’s universal algebra construction, which is relevant e.g. for the BRST/BV formalism. We further develop a homotopy theoretical generalization of algebraic quantum field theory with a particular focus on the homotopy-coherent Einstein causality axiom. We provide examples of such homotopy-coherent theories via (1) smooth normalized cochain algebras on ∞-stacks, and (2) fiber-wise groupoid cohomology of a category fibered in groupoids with coefficients in a strict quantum field theory.


Benini, M., Schenkel, A., & Woike, L. (2019). Homotopy theory of algebraic quantum field theories. Letters in Mathematical Physics, 109(7), 1487-1532.

Journal Article Type Article
Acceptance Date Dec 22, 2018
Online Publication Date Jan 16, 2019
Publication Date 2019-07
Deposit Date Jan 11, 2019
Publicly Available Date Jan 17, 2019
Journal Letters in Mathematical Physics
Print ISSN 0377-9017
Electronic ISSN 1573-0530
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 109
Issue 7
Pages 1487-1532
Keywords Mathematical Physics; High Energy Physics - Theory; Algebraic Topology;
Public URL
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