prof. L. Dąbrowski, SISSA, Trieste, Italy

Almost commutative geometry of the Standard Model

By functions on a noncommutative (or `quantum') space one usually means a suitable algebra of operators. Then the smooth and metric structures can be described in terms of a spectral triple which involves an analogue of the Dirac operator. The Standard Model of fundamental particles in physics can be understood as the almost commutative geometry, the exterior part of which is the canonical spectral triple on a spin manifold and the finite inner part a quantum analogue of the de-Rham-Hodge spectral triple.