Quantum field theories on categories fibered in groupoids

Abstract

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles, connections and spin structures. Using right Kan extensions, we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory. The same constructions can be performed in a homotopy theoretic framework by using homotopy right Kan extensions, which allows us to obtain first toy-models of homotopical quantum field theories resembling some aspects of gauge theories.

v2: 41 pages. Final version published in Communications in Mathematical Physics

References in corpus (6)

• Homotopy colimits and global observables in Abelian gauge theory
• The universal C*-algebra of the electromagnetic field
• Abelian duality on globally hyperbolic spacetimes
• The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields
• Global anomalies on Lorentzian space-times
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Cited by in corpus (9)

• Homotopy theory of algebraic quantum field theories
• Operads for algebraic quantum field theory
• The stack of Yang-Mills fields on Lorentzian manifolds
• Linear Yang-Mills theory as a homotopy AQFT
• Higher Structures in Algebraic Quantum Field Theory
• Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds
• Snowmass White Paper: The Quest to Define QFT
• Intertwining operators for symmetric hyperbolic systems on globally hyperbolic manifolds
• Spacetimes categories and disjointness for algebraic quantum field theory