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Homotopy theory of algebraic quantum field theories

Benini, Marco; Schenkel, Alexander; Woike, Lukas


Marco Benini

Alexander Schenkel

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.

Journal Article Type Article
Publication Date 2019-07
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
Publisher URL


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