dorsal/arxiv
View SchemaUn-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space
| Authors | Jian-Zu Zhang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602179 |
| URL | https://arxiv.org/abs/quant-ph/0602179 |
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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"abstract": "An extensively tacit understandings of equivalency between the deformed\nHeisenberg-Weyl algebra in noncommutative space and the undeformed\nHeisenberg-Weyl algebra in commutative space is elucidated. Equivalency\nconditions between two algebras are clarified. It is explored that the deformed\nalgebra related to the undeformed one by a non-orthogonal similarity\ntransformation. Furthermore, non-existence of a unitary similarity\ntransformation which transforms the deformed algebra to the undeformed one is\ndemonstrated. The un-equivalency theorem between the deformed and the\nundeformed algebras is fully proved. Elucidation of this un-equivalency theorem\nhas basic meaning both in theory and practice.",
"arxiv_id": "quant-ph/0602179",
"authors": [
"Jian-Zu Zhang"
],
"categories": [
"quant-ph"
],
"title": "Un-equivalency Theorem of Deformed Heisenberg-Weyl\u0027s Algebra in Noncommutative Space",
"url": "https://arxiv.org/abs/quant-ph/0602179"
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