#math.oa

[arsphysica]

"The spectral action in noncommutative geometry naturally implements an ultraviolet cut-off, by counting the eigenvalues of a (generalized) Dirac operator lower than an energy of unification. Inverting the well known question "how to hear the shape of a drum ?", we ask what drum can be designed by hearing the truncated music of the spectral action ? This makes sense because the same Dirac operator also determines the metric, via Connes distance. The latter thus offers an original way to implement the high-momentum cut-off of the spectral action as a short distance cut-off on space. This is a non-technical presentation of the results of this http URL."

[arsphysica]

"The aim of the present paper is to present the construction of a general family of $C^{\ast}$-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 $C^{\ast}$-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 $C^{\ast}$-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."