Coulomb solutions from improper pseudo-unitary free gauge field operator translations

TL;DR

This paper explores the representation of Coulomb fields in quantum gauge theories using a pseudo-unitary framework, addressing fundamental issues in quantum field theory and introducing generalized gauge transformations.

Contribution

It introduces a novel approach to describe Coulomb solutions via improper pseudo-unitary operators and generalizes gauge transformations within a Krein space structure.

Findings

Coulomb fields can be modeled as superpositions of pseudo-photons in a Krein space.

Generalized gauge transformations produce coherent states of gauge fields.

The approach offers insights into the representation problem of canonical commutation relations.

Abstract

Fundamental problems of quantum field theory related to the representation problem of canonical commutation relations are discussed within a gauge field version of a van Hove-type model. The Coulomb field generated by a static charge distribution is described as a formal superposition of time-like pseudo-photons in Fock space with a Krein structure. In this context, a generalization of operator gauge transformations is introduced to generate coherent states of abelian gauge fields interacting with a charged background.