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 leaflabelled 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 qanalogue 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 



00103616


Volume/pages 



304:2(2011), p. 369393


ISI 



000290229600003


Full text (Publishers DOI) 


 
