Bonn 2010 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Noncommutative Geometry

MP 10.1: Talk

Thursday, March 18, 2010, 08:30–08:55, JUR H

Spectral Triples of Holonomy Loops — •Jesper Grimstrup — Niels Bohr Institute, Copenhagen, Denmark

In my talk I will review the construction of a spectral triple over a configuration space of connections. The spectral triple construction is related to quantum gravity since the interaction of the algebra with the Dirac type operator reproduces the structure of the Poisson bracket of General Relativity when formulated in terms of Ashtekar variables. I will show how the Dirac Hamiltonian in 3+1 dimensions emerge naturally from the construction in a semi-classical approximation. This indicates that the framework includes canonical matter degrees of freedom. Also, I will show how an operator is constructed which in the semi-classical limit gives the constraints of canonical gravity.