Fields, observables and gauge transformations II

Abstract

We wish to study the construction of charge-carrying fields given the representation of the observable algebra in the sector of states of zero charge. It is shown that the set of those covariant sectors which can be obtained from the vacuum sector by acting with “localized automorphisms” has the structure of a discrete Abelian group . An algebra of fields $$\mathfrak{F}$$ can be defined on the Hilbert space of a representation π of the observable algebra $$\mathfrak{A}$$ which contains each of the above sectors exactly once. The dual group of acts as a gauge group on $$\mathfrak{F}$$ in such a way that $$\pi (\mathfrak{A})$$ is the gauge invariant part of $$\mathfrak{F}.\mathfrak{F}$$ is made up of Bose and Fermi fields and is determined uniquely by the commutation relations between spacelike separated fields.