Fields, observables and gauge transformations I

Abstract

Starting from an algebra of fields $$\mathfrak{F}$$ and a compact gauge group of the first kind ℊ, the observable algebra $$\mathfrak{A}$$ is defined as the gauge invariant part of $$\mathfrak{F}$$ . A gauge group of the first kind is shown to be automatically compact if the scattering states are complete and the mass and spin multiplets have finite multiplicity. Under reasonable assumptions about the structure of $$\mathfrak{F}$$ it is shown that the inequivalent irreducible representations of $$\mathfrak{A}$$ (“sectors”) which occur are in one-to-one correspondence with the inequivalent irreducible representations of ℊ and that all of them are “strongly locally equivalent”. An irreducible representation of $$\mathfrak{A}$$ satisfies the duality property only if the sector corresponds to a 1-dimensional representation of ℊ. If ℊ is Abelian the sectors are connected to each other by localized automorphisms.