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

TL;DR

This paper explores U(1)-invariant field theories with normal field operators, revealing the existence of particles and antiparticles, and analyzing the structure of creation and annihilation operators, especially in the q-deformed case.

Contribution

It demonstrates that U(1) invariance implies particles and antiparticles originate from the same state, and characterizes the structure of related creation and annihilation operators.

Findings

Field operators commute with their adjoints, indicating charged bosonic particles.

Particles and antiparticles are associated with the same physical state due to U(1) invariance.

Factorized creation and annihilation operators relate to q-deformed commutation relations.

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.