Publication
Title
Distortion of the Poisson bracket by the noncommutative Planck constants
Author
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.
Language
English
Source (journal)
Communications in mathematical physics. - Heidelberg
Publication
Heidelberg : 2011
ISSN
0010-3616
Volume/pages
304:2(2011), p. 369-393
ISI
000290229600003
Full text (Publisher's DOI)
UAntwerpen
 Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address