Some Consequences of a Generalization to Heisenberg Algebra in Quantum Electrodynamics

TL;DR

This paper explores how modifying the Heisenberg algebra to include a minimal observable length affects quantum electrodynamics, leading to states that violate traditional uncertainty relations and suggesting the need for a minimal observable momentum.

Contribution

It demonstrates that incorporating a minimal observable length into the Heisenberg algebra alters quantum states and implies the necessity of a minimal observable momentum in quantum electrodynamics.

Findings

States violating the Heisenberg uncertainty principle due to minimal length

Necessity of including minimal momentum in generalized uncertainty principles

Implications for the quantization process of the electromagnetic field

Abstract

In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical field, renders states in which the uncertainties in the two quadrature components violate the usual Heisenberg uncertainty relation. Hence in this context it may be asserted that any physically realistic generalization of the uncertainty principle must include, not only a minimal observable length, but also a minimal observable momentum.