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EnglishMotivated 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.
| Titolo: | Homotopy theory of algebraic quantum field theories |
| Autori: | |
| Data di pubblicazione: | 2019 |
| Rivista: | |
| Handle: | http://hdl.handle.net/11567/947094 |
| Appare nelle tipologie: | 01.01 - Articolo su rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | |
|---|---|---|---|
| arXiv 1805.08795v2 [math-ph] 16012019.pdf | Pre-print | Open Access Visualizza/Apri |
http://hdl.handle.net/11567/947094
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