Title Distortion of the Poisson bracket by the noncommutative Planck constants Author Ruuge, Artur E. Van Oystaeyen, Freddy Faculty/Department Faculty of Sciences. Mathematics and Computer Science Publication type article Publication 2011 Heidelberg , 2011 Subject Mathematics Physics Source (journal) Communications in mathematical physics. - Heidelberg Volume/pages 304(2011) :2 , p. 369-393 ISSN 0010-3616 ISI 000290229600003 Carrier E Target language English (eng) Full text (Publishers DOI) Affiliation University of Antwerp Abstract 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. E-info http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000290229600003&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000290229600003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle