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The idea that the coordinates of space itself may satisfy non-trivial commutation relations goes back to the very early days of quantum mechanics. In this talk I will review the various motivations for introducing non-commutative geometry, the connection with non-abelian gauge theories and the expectations related to physics beyond the standard model.
However, I want also to warn the audience that, up to now, no novel physical results have been obtained using this approach.
Angelo Esposito