Spectral Action for Scalar Perturbations of Dirac OperatorsReport as inadecuate

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Letters in Mathematical Physics

, Volume 98, Issue 3, pp 333–348

First Online: 21 July 2011Received: 23 January 2011Revised: 07 April 2011Accepted: 26 April 2011


We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey–de Witt coefficients and make explicit calculations for the case of n-spheres with a completely symmetric Dirac. In the special case of dimension 3, when such perturbation corresponds to the completely antisymmetric torsion, we carry out the noncommutative calculation following Chamseddine and Connes J Geom Phys 57:121, 2006 and study the case of SUq2.

Mathematics Subject Classification 200058B34 81T75 A. Sitarz was partially supported by MNII grants 189-6.PRUE-2007-7 and N 201 1770 33.

A. Zając supported by a project operated within the Foundation for Polish Science IPP Programme -Geometry and Topology in Physical Models- co-financed by the EU European Regional Development Fund, Operational Program Innovative Economy 2007–2013.

Keywordsspectral geometry noncommutative geometry  Download to read the full article text

Author: Andrzej Sitarz - Artur Zając

Source: https://link.springer.com/

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