Fractional Angular Momentum in Noncommutative Space

TL;DR

This paper investigates how noncommutative geometry affects bosonic systems, revealing that angular momentum spectra can exhibit fractional eigenvalues due to space and momentum noncommutativity.

Contribution

It introduces a new type of boson commutation relations in noncommutative space and analyzes their impact on angular momentum spectra, showing fractional eigenvalues.

Findings

Angular momentum spectrum exhibits fractional eigenvalues.

New boson commutation relations derived for noncommutative space.

Influence of noncommutativity on quantum dynamics discussed.

Abstract

In noncommutative space to maintain Bose-Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by generalizing one-particle quantum mechanics it is explored that the consistent ansatz of commutation relations of phase space variables should simultaneously include space-space noncommutativity and momentum-momentum noncommutativity, and a new type of boson commutation relations at the deformed level is obtained. Consistent perturbation expansions of deformed annihilation-creation operators are obtained. The influence of the new boson commutation relations on dynamics is discussed. The non-perturbation and perturbation property of the orbital angular momentum of two-dimensional system are investigated. Its spectrum possesses fractional eigen values and fractional intervals.