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49. A.Sitarz
Spectral action and neutrino mass
European Physics Letters, vol. 86, p. 10007 (2009).
[abstract] [preprint] [journal] [download]

We propose the extension of the spectral action principle to fermions and show that the neutrino mass terms then appear naturally as next-order corrections.

50. B.Iochum, C.Levy, A.Sitarz
Spectral action on SUq(2)
Commun. Math. Phys., vol. 289, pp. 107-155 (2009).
[abstract] [preprint] [journal] [download]

The spectral action on the equivariant real spectral triple over A(SUq(2))SUq(2) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of the sphere \mathbbS3S3.

51. Nicolas Franco
Survey of Gravity in Non-Commutative Geometry
Topology, Quantum fields theory & Cosmology, Hermann, pp. 313-329 (2009).
[abstract] [preprint]

We present a survey of the application of Cones' Non-Commutative Geometry to gravitation. Bases of the theory and Euclidian gravity models are reviewed. Then we discuss the problem of a Lorentzian generalization of the theory and review existing attempts of solution.

52. Sebastian J. Szybka
Chaos and Vacuum Gravitational Collapse
Proceedings of the Spanish Relativity Meeting 2008, AIP Conf. Proc., vol. 1122, pp. 172-178 (2009).
[abstract] [journal]

The numerical evidence for chaotic behavior in vacuum gravitational collapse is presented. The collapse is studied in five dimensional vacuum spacetimes satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz.

53. A. Sitarz
Twisted Dirac operators over quantum spheres
J.Math.Phys, vol. 49, p. 0335092008 (2008).
[abstract] [preprint] [journal]

We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.

54. A.Sitarz
3 1/2 Lectures on Noncommutative Geometry
Acta Polytechnica, vol. 48, pp. 34-55 (2008).
[abstract] [journal] [download]

We present a short overview of noncommutative geometry. Starting with C* algebras and noncommutative differential forms we pass to K-theory, K-homology and cyclic (co)homology, and we finish with the notion of spectral triples and the spectral action.

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