Homotopy theory of algebraic quantum field theories

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.

arXiv commentv2: 38 pages - Added appendix on examples for local-to-global constructions. Final version published in Letters in Mathematical Physics

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Cited by in corpus (20)

• Operads for algebraic quantum field theory
• Linear Yang-Mills theory as a homotopy AQFT
• Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds
• Categorification of algebraic quantum field theories
• Snowmass White Paper: The Quest to Define QFT
• Algebraic field theory operads and linear quantization
• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• A Lorentzian renormalisation group equation for gauge theories
• Quantization of Lorentzian free BV theories: factorization algebra vs algebraic quantum field theory
• Strictification theorems for the homotopy time-slice axiom
• Relative Cauchy evolution for linear homotopy AQFTs
• Green hyperbolic complexes on Lorentzian manifolds
• Homotopy theory of net representations
• Spacetimes categories and disjointness for algebraic quantum field theory
• Lorentzian bordisms in algebraic quantum field theory
• On the equivalence of AQFTs and prefactorization algebras
• Classical BV formalism for group actions
• Space-time singularities and the theory of retracts
• The linear CS/WZW bulk/boundary system in AQFT
• A new topological perspective of expanding space-times with applications to cosmology