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arXiv · hep-th/0612254

Un-equivalency Theorem between Deformed and undeformed Heisenberg-Weyl's Algebras

Jian-Zu Zhang
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Abstract

Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. First the un-equivalency theorem between two algebras is proved: the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation is explored; furthermore, non-existence of a unitary similarity transformation which transforms the deformed algebra to the undeformed one is demonstrated. Secondly the uniqueness of realizing the deformed phase space variables via the undeformed ones is elucidated: both the deformed Heisenberg-Weyl algebra and the deformed bosonic algebra should be maintained under a linear transformation between two sets of phase space variables which fixes that such a linear transformation is unique. Elucidation of this un-equivalency theorem has basic meaning both in theory and experiment.

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Jian-Zu Zhang. 2006-12-23. Un-equivalency Theorem between Deformed and undeformed Heisenberg-Weyl's Algebras. https://doi.org/10.1016/j.physletb.2006.06.040

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