Dixmier traces on noncompact isospectral deformations

Details Dixmier traces on noncompact isospectral deformations Dixmier traces on noncompact isospectral deformations

2005-07-21

arxiv.org/abs/hep-th/0507206v2

J.Funct.Anal. 237 (2006) 507-539

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, no figures; several minor improvements, to appear in J. Funct. Anal

Scientific paper

We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group $R^l$. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of $R^l$, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.

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