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arXiv · 1201.1583

The DFR-Algebra for Poisson Vector Bundles

Michael Forger·Daniel V. Paulino
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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 space-time algebra" first introduced by Doplicher, Fredenhagen and Roberts. To this end, we first review, within the $C^*$-algebra context, the Weyl-Moyal 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 DFR-model, this method yields a "fiberwise quantization" of general Poisson manifolds.

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Michael Forger, Daniel V. Paulino. 2012-01-07. The DFR-Algebra for Poisson Vector Bundles. https://arxiv.org/abs/1201.1583

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