Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Un-equivalency Theorem between Deformed and undeformed Heisenberg-Weyl's
  Algebras   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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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-ex