FIELDS, OBSERVABLES AND GAUGE TRANSFORMATIONS .I.

Starting from an algebra of fields {Mathematical expression} and a compact gauge group of the first kind g{script}, the observable algebra {Mathematical expression} is defined as the gauge invariant part of {Mathematical expression}. 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 {Mathematical expression} it is shown that the inequivalent irreducible representations of {Mathematical expression} (sectors") which occur are in one-to-one correspondence with the inequivalent irreducible representations of g{script} and that all of them are "strongly locally equivalent". An irreducible representation of {Mathematical expression} satisfies the duality property only if the sector corresponds to a 1-dimensional representation of g{script}. If g{script} is Abelian the sectors are connected to each other by localized automorphisms. © 1969 Springer-Verlag."