Quantum mechanics of the nonrelativistic Yang model

TL;DR

This paper explores the quantum mechanics of a phase space realization of the Yang model, highlighting how noncommutative geometry and uncertainty relations depend on coupling constants, with analysis of free particle and harmonic oscillator dynamics.

Contribution

It provides a leading-order quantum mechanical analysis of the Yang model in phase space, emphasizing the role of coupling constant signs in noncommutative geometry and dynamics.

Findings

Deformation of Heisenberg uncertainty relations depends on coupling signs

Dynamics of free particle and harmonic oscillator vary with coupling signs

Results reveal sign-dependent noncommutative geometric effects

Abstract

We discuss, at leading order in $\hbar$, the quantum mechanics of a specific realization in phase space of the Yang model describing noncommutative geometry in a curved background. In particular, we show how the deformation of the Heisenberg uncertainty relations crucially depends on the signs of the coupling constants of the model. We also discuss the dynamics of the free particle and of the harmonic oscillator. Also in this case the results depend on the signs of the coupling constants.