Gauge transformations of a relativistic field of quantum harmonic oscillators

TL;DR

This paper rigorously studies gauge transformations in a relativistic quantum harmonic oscillator field, revealing how these transformations can generate freely-propagating wave fields from coherent states.

Contribution

It introduces a mathematically rigorous framework for gauge transformations in relativistic quantum harmonic oscillator fields, including the construction of differentiable manifolds of coherent states.

Findings

Gauge transformations can produce freely-propagating wave fields.

A differentiable manifold of coherent states is constructed.

Wave functions generate Frechet-differentiable fields.

Abstract

A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a Frechet-differentiable field of wave functions. Starting from a coherent wave function one obtains a two-dimensional differentiable manifold of coherent vector states. As an illustration it is shown that the gauge transformation can be chosen in such a way that the resulting fields describe a freely-propagating wave.