Generalized Uncertainty Principle and Quantum Electrodynamics

TL;DR

This paper explores how a generalized uncertainty principle influences the quantization of the electromagnetic field, leading to a deformed dispersion relation and modifications in the photon concept and energy calculations.

Contribution

It introduces a framework for quantizing the electromagnetic field under a generalized uncertainty principle, revealing new operator dependencies and altered energy spectra.

Findings

Existence of a Fock space under the generalized uncertainty principle

Modification of creation and annihilation operators

Deformed dispersion relation for photons

Abstract

In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisenberg algebra, and hence the Hamiltonian is not anymore diagonal in the occupation number representation. Additionally, we show the changes that the energy expectation value suffers as result of the presence of an extra term in the uncertainty principle. The existence of a deformed dispersion relation is also proved.