Abstract:
We study noncommutative geometry from a metric point of view by
constructing examples of spectral triples and explicitly calculating Connes's
spectral distance between certain associated pure states. After considering
instructive nite-dimensional spectral triples, the noncommutative geometry
of the in nite-dimensional Moyal plane is studied. The corresponding
spectral triple is based on the Moyal deformation of the algebra of Schwartz
functions on the Euclidean plane.