Endomorphisms and automorphisms of locally covariant quantum field theories

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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.
Original languageEnglish
Article number1350008
Pages (from-to)1-47
Number of pages47
JournalReviews in Mathematical Physics
Issue number5
Publication statusPublished - Jun 2013


  • mathematical physics;
  • general relativity;
  • quantum cosmology;

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