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Distortion of the Poisson Bracket by the Noncommutative Planck Constants
- Source :
- Commun. Math. Phys. 304, 369 -- 393 (2011)
- Publication Year :
- 2009
-
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.
- Subjects :
- Mathematical Physics
Mathematics - Quantum Algebra
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Commun. Math. Phys. 304, 369 -- 393 (2011)
- Publication Type :
- Report
- Accession number :
- edsarx.0910.2949
- Document Type :
- Working Paper