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

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Jian-Zu Zhang

High Energy Physics - Theory · Submitted 23 Dec 2006

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDhep-th/0612254 (version 1)
Pith IDVIMN7CJP, Pith's permanent record of this paper and its review
CitationJian-Zu Zhang. "Un-equivalency Theorem between Deformed and undeformed Heisenberg-Weyl's Algebras." arXiv:hep-th/0612254 (2006). https://pith.science/paper/VIMN7CJP
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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Two fundamental issues about the relation between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed one in commutative space are elucidated. contribution 0.77 0.88 0.10 asserted 0.99
s1 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. result 0.89 0.93 0.75 asserted 1.00
s2 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. result 0.95 0.87 0.21 asserted 1.00
s3 Elucidation of this un-equivalency theorem has basic meaning both in theory and experiment. interpretation 1.00 0.33 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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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