Un-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space
Quantum Physics
2007-05-23 v1
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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Cite
@article{arxiv.quant-ph/0602179,
title = {Un-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space},
author = {Jian-Zu Zhang},
journal= {arXiv preprint arXiv:quant-ph/0602179},
year = {2007}
}
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9 pages