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arXiv · 1805.08795

Homotopy theory of algebraic quantum field theories

Marco Benini·Alexander Schenkel·Lukas Woike
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Abstract

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 $\infty$-stacks, and (2) fiber-wise groupoid cohomology of a category fibered in groupoids with coefficients in a strict quantum field theory.

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Marco Benini, Alexander Schenkel, Lukas Woike. 2019-01-16. Homotopy theory of algebraic quantum field theories. https://doi.org/10.1007/s11005-018-01151-x

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