Deformed algebraic structure of angular momenta: GUP perspective

TL;DR

This paper reviews how quantum gravity theories suggest a minimal length scale leading to a modified uncertainty principle, which in turn deforms the algebra of angular momentum and impacts atomic spectra.

Contribution

It introduces a deformed algebraic structure of angular momenta based on the GUP, extending minimal length concepts to angular resolution and analyzing their effects.

Findings

Modified angular momentum algebra due to GUP

Impact on hydrogen atom spectra

Comparison between standard and GUP-modified algebra

Abstract

The prediction of a minimal length scale by various quantum gravity candidates (such as string/M theory, Doubly Special Relativity, Loop Quantum Gravity and others) have suggested modification of Heisenberg Uncertainty Principle (HUP), resulting in the Generalized Uncertainty Principle (GUP). In this short review, we investigate the origins of the GUP and examine higher-order models, focusing on the linear plus quadratic form of the GUP. We extend the concept of minimal length to minimal angular resolution, which plays a crucial role in modifying angular momentum and its associated algebra. A comparison is made between the standard angular momentum commutator algebra and that modified by the GUP. Finally, we review its application in the hydrogen atom spectra and and discuss future endeavors.