Distortion of the Poisson bracket by the noncommutative Planck constants
Distortion of the Poisson bracket by the noncommutative Planck constants
Faculty of Sciences. Mathematics and Computer Science

article

2011
Heidelberg
, 2011

Mathematics

Physics

Communications in mathematical physics. - Heidelberg

304(2011)
:2
, p. 369-393

0010-3616

000290229600003

E

English (eng)

University of Antwerp

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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