文献类型：期刊文献

英文题名：Un-equivalency theorem between deformed and undeformed Heisenberg-Weyl's algebras

作者：Zhang, Jian-Zia

机构：[1]E China Univ Sci & Technol, Inst Theoret Phys, Shanghai 200237, Peoples R China

年份：2006

卷号：639

期号：3-4

起止页码：403

外文期刊名：PHYSICS LETTERS B

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000239676500042)】；

语种：英文

摘要：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. (c) 2006 Elsevier B.V. All rights reserved.