The U(1)-invariant field theories with normal field operators

Abstract

In this paper we consider a very general U(1)-invariant field theory such that a field operator commutes with its adjoint, what corresponds to a theory of a charged bosonic particle. We show that from such an invariance follows the existence of particles and antiparticles associated to the same physical state. The field operator always turns out to be a sum of a particle creation and an antiparticle annihilation operators. We study in detail the case when creation and annihilation operators factorize and show that such operators are closely related to q-deformed commutation relations.