On the local implementations of gauge symmetries in local quantum theory (Q1091578)

The author proves a uniqueness theorem for the local implementations of gauge transformations in a local quantum theory where the local algebras of field operators fulfill the split property [see \textit{S. Doplicher} and \textit{R. Longo}, Commun. Math. Phys. 88, 399-409 (1983; Zbl 0523.46046)]. If \({\mathcal U}\) and \({\mathcal V}\) are two local covariant implementations for a pair \({\mathcal O}_ 1,{\mathcal O}_ 2\) of double cones, one can find a unitary operator realizing the equivalence between them. This unitary belongs to the algebra of observables localized in a double cone containing \({\mathcal O}_ 2\) in its interior and commutes with the field localized in a double cone contained in the interior of \({\mathcal O}_ 1\).