Inequivalence of quantum Dirac fields of different masses and the underlying general structures involved

Abstract

A family of irreducible representations of the canonical anticommutation relations over an abstract Hilbert space indexed by a set of bounded linear operators is presented and a theorem on the mutual equivalence of them is established. As an application of the theorem, it is proved that quantum Dirac fields of different masses are mutually inequivalent. Moreover, a new class of irreducible representations of the CAR over a Hilbert space, which includes, as a special case, time-zero quantum Dirac fields, is constructed.