Transverse Radiation realized as Deformed Harmonic Oscillators

TL;DR

This paper develops a quantum field theory framework using q-deformed harmonic oscillators, exploring how deformation affects field properties, vacuum energy, and polarization relations in a novel way compared to standard quantum electrodynamics.

Contribution

It introduces a formalism for quantized radiation fields based on q-deformed oscillators, extending the mathematical structure of quantum electrodynamics with deformed commutation relations.

Findings

Deformed commutation relations alter the structure of the Fock space.

The vacuum energy and momentum relations are modified by the deformation.

Electric field commutators resemble q-deformed uncertainty relations.

Abstract

We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this formalism in terms of basic numbers familiar from the theory of quantum groups. Expressions for the Hamiltonian and momentum arising from deformed Heisenberg relations are obtained and their consequences investigated. The energy momentum properties of the vacuum state are studied. The commutation relation for the fields is shown to involve polarization sums more intricate than those encountered in standard quantum electrodynamics, thus requiring explicit representations of polarization vectors. The electric field commutation rules are investigated under simplifying assumptions of polarization states, and the commutator in the deformed theory in this case is shown to be reminiscent of the coordinate-momentum uncertainty relation in the theory of q-deformed quantum oscillators.