Un-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space

Jian-Zu Zhang

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Un-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space

Jian-Zu Zhang

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Abstract

An extensively tacit understandings of equivalency between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed Heisenberg-Weyl algebra in commutative space is elucidated. Equivalency conditions between two algebras are clarified. It is explored that the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation. Furthermore, non-existence of a unitary similarity transformation which transforms the deformed algebra to the undeformed one is demonstrated. The un-equivalency theorem between the deformed and the undeformed algebras is fully proved. Elucidation of this un-equivalency theorem has basic meaning both in theory and practice.

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Jian-Zu Zhang. 2006-02-22. Un-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space. https://arxiv.org/abs/quant-ph/0602179

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