Letters in Mathematical Physics

, Volume 98, Issue 3, pp 333–348

Spectral Action for Scalar Perturbations of Dirac Operators

Open Access
Article

DOI: 10.1007/s11005-011-0498-5

Cite this article as:
Sitarz, A. & Zając, A. Lett Math Phys (2011) 98: 333. doi:10.1007/s11005-011-0498-5

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 SUq(2).

Mathematics Subject Classification (2000)

58B34 81T75 

Keywords

spectral geometry noncommutative geometry 
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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Institute of PhysicsJagiellonian UniversityKrakówPoland

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