Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 077, 17 pages      arXiv:1003.1210      https://doi.org/10.3842/SIGMA.2010.077
Contribution to the Special Issue “Noncommutative Spaces and Fields”

A Canonical Trace Associated with Certain Spectral Triples

Sylvie Paycha
Laboratoire de Mathématiques, 63177 Aubière Cedex, France

Received March 11, 2010, in final form September 13, 2010; Published online September 29, 2010

Abstract
In the abstract pseudodifferential setup of Connes and Moscovici, we prove a general formula for the discrepancies of zeta-regularised traces associated with certain spectral triples, and we introduce a canonical trace on operators, whose order lies outside (minus) the dimension spectrum of the spectral triple.

Key words: spectral triples; zeta regularisation; noncommutative residue; discrepancies.

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