The theory of superselection rules. I. A class of inequivalent, irreducible *-representations of the canonical commutation relations of the free electromagnetic field

Abstract

We begin here the rigorous construction of new superselection sectors for the free quantum electromagnetic field by exhibiting a wide class of inequivalent irreducible *‐representations of the canonical commutation relations of the electromagnetic field. The *‐representations constructed here satisfy all the axioms of Haag and Kastler, except possibly Poincaré covariance. In a forthcoming paper, the construction of the new superselection sectors is completed with the study of the spectrum condition for the *‐representations.