Endomorphisms and automorphisms of locally covariant quantum field theories

Understand

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.