We discuss, at leading order in ℏ, 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 relation 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.
Quantum mechanics of the nonrelativistic Yang model
Mignemi, S.
2025-01-01
Abstract
We discuss, at leading order in ℏ, 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 relation 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.
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