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A Constraint between Noncommutative Parameters of Quantum Theories in Noncommutative Space

Jian-Zu Zhang
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Abstract

In two-dimensional noncommutive space for the case of both position - position and momentum - momentum noncommuting, a constraint between noncommutative parameters is investigated. The related topic of guaranteeing Bose - Einstein statistics in noncommutive space in the general case are elucidated: Bose - Einstein statistics is guaranteed by the deformed Heisenberg - Weyl algebra itself, independent of dynamics. A special character of a dynamical system is represented by a constraint between noncommutative parameters. The general feature of the constraint for any system is a direct proportionality between noncommutative parameters with a proportional coefficient depending on characteristic parameters of the system under study. The constraint for a harmonic oscillator is illustrated.

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Jian-Zu Zhang. 2007-04-12. A Constraint between Noncommutative Parameters of Quantum Theories in Noncommutative Space. https://arxiv.org/abs/quant-ph/0701166

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