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arXiv 0810.20912008-10-12hep-thmath.QA

A unitary invariant in Riemannian geometry

Alain Connes

备注：: 25 pages, 1 Figure
发表信息：: Int.J.Geom.Meth.Mod.Phys.5:1215-1242,2008
DOI：: 10.1142/S0219887808003284

英文摘要：

We introduce an invariant of Riemannian geometry which measures the relative position of two von Neumann algebras in Hilbert space, and which, when combined with the spectrum of the Dirac operator, gives a complete invariant of Riemannian geometry. We show that the new invariant plays the same role with respect to the spectral invariant as the Cabibbo--Kobayashi--Maskawa mixing matrix in the Standard Model plays with respect to the list of masses of the quarks.

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