Schwinger's Model of Angular Momentum with GUP

TL;DR

This paper explores how the generalized uncertainty principle (GUP) affects angular momentum in quantum systems, specifically modifying the harmonic oscillator and deriving GUP-adjusted angular momentum algebra and Clebsch-Gordan coefficients.

Contribution

It introduces a GUP-modified angular momentum algebra based on Schwinger's model and explicitly calculates the CG coefficients, showing they remain unchanged up to quadratic GUP.

Findings

GUP modifies the harmonic oscillator operators

GUP-adjusted angular momentum algebra is constructed

CG coefficients are unaffected up to quadratic GUP

Abstract

We study the generalized uncertainty principle (GUP) modified simple harmonic oscillator (SHO) in the operator formalism by considering the appropriate form of the creation and annihilation operators $ A, A^\dagger $. The angular momentum algebra is then constructed using Schwinger's model of angular momentum with two independent GUP modified SHOs. With the GUP modified angular momentum algebra, we discuss coupling of angular momentum for a two-particle composite system. Further, we calculate the Clebsch-Gordan (CG) coefficients for a two-particle system explicitly. Our results show that the CG coefficients do not receive any corrections upto quadratic GUP.