A Constraint between Noncommutative Parameters of Quantum Theories in Noncommutative Space

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. ∗ E-mail: [email protected] Fax: +86-21-64251138 Tel: +86-21-64252613