The DFRAlgebra for Poisson Vector Bundles
Abstract
The aim of the present paper is to present the construction of a general family of $C^*$algebras that includes, as a special case, the "quantum spacetime algebra" first introduced by Doplicher, Fredenhagen and Roberts. To this end, we first review, within the $C^*$algebra context, the WeylMoyal quantization procedure on a fixed Poisson vector space (a vector space equipped with a given bivector, which may be degenerate). We then show how to extend this construction to a Poisson vector bundle over a general manifold $M$, giving rise to a $C^*$algebra which is also a module over $C_0(M)$. Apart from including the original DFRmodel, this method yields a "fiberwise quantization" of general Poisson manifolds.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 arXiv:
 arXiv:1201.1583
 Bibcode:
 2012arXiv1201.1583F
 Keywords:

 Mathematics  Operator Algebras;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics;
 46L65;
 46L08;
 53D55
 EPrint:
 13 pages