, Volume 98, Issue 3, pp 333-348,
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Spectral Action for Scalar Perturbations of Dirac Operators

Abstract

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 SU q (2).

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.