Endomorphisms and automorphisms of locally covariant quantum field theories

Abstract

In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of *-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covariant theories that obey standard assumptions in Minkowski space, including energy compactness, have no proper endomorphisms (i.e., all endomorphisms are automorphisms) and have a compact automorphism group. Further, it is shown how the endomorphisms and automorphisms of a locally covariant theory may, in principle, be classified in any single spacetime. As an example, the endomorphisms and automorphisms of a system of finitely many free scalar fields are completely classified.

v2 45pp, expanded to include additional results; presentation improved and an error corrected. To appear in Rev Math Phys

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Cited by in corpus (18)

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• Dynamical locality of the free scalar field
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• Locally covariant quantum field theory and the problem of formulating the same physics in all spacetimes
• The split property for locally covariant quantum field theories in curved spacetime
• Dynamical locality of the free Maxwell field
• Model-independent comparison between factorization algebras and algebraic quantum field theory on Lorentzian manifolds
• Quantum field theories on categories fibered in groupoids
• Locally covariant quantum field theory with external sources
• Abelian duality on globally hyperbolic spacetimes
• Snowmass White Paper: The Quest to Define QFT
• Presheaves of superselection structures in curved spacetimes
• The Semiclassical Einstein Equation on Cosmological Spacetimes
• Global anomalies on Lorentzian space-times
• An analogue of the Coleman-Mandula theorem for quantum field theory in curved spacetimes
• Locally covariant quantum field theory and the spin-statistics connection
• Locality in Abelian gauge theories over globally hyperbolic spacetimes