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Title
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Distortion of the Poisson bracket by the noncommutative Planck constants
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Author
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Abstract
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| In this paper we introduce a kind of noncommutative neighbourhood of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of generators indexed by planar binary leaf-labelled trees. The associated graded algebra (the classical shadow) is interpreted as a distortion of the algebra of classical observables of a physical system. It is proven that there exists a q-analogue of the Weyl quantization, where q is a matrix of formal variables, which induces a nontrivial noncommutative analogue of a Poisson bracket on the classical shadow. |
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Language
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English
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Source (journal)
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Communications in mathematical physics. - Heidelberg, 1965, currens
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Publication
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Heidelberg
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Springer
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2011
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ISSN
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0010-3616
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DOI
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10.1007/S00220-011-1230-0
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Volume/pages
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304
:2
(2011)
, p. 369-393
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ISI
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000290229600003
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Full text (Publisher's DOI)
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