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GR: Fachverband Gravitation und Relativitätstheorie

GR 3: Quantum Gravity II

GR 3.6: Vortrag

Montag, 29. Februar 2016, 18:25–18:45, VMP6 HS A

Quantum Gravity a la Aharonov-Bohm — •Marcin Kisielowski — University of Erlangen-Nürnberg, Erlangen, Germany

In the Regge approximation to General Relativity a space-time is a simplicial complex equipped with a metric structure determined by the edge lengths. For each such Regge space-time we construct a smooth manifold equipped with flat connection and a compatible tetrad. The resulting manifold is not simply connected -- we will say that it is a manifold with defects. Although the connection is flat a parallel transport around a closed loop can be non-trivial. This is a mathematical basis of the Aharonov-Bohm effect: the magnetic field is zero outside thin and long solenoid but the holonomy around a loop encircling the solenoid is non-trivial. Using this analogy we introduce a (distributional) curvature on the simplicial complex. This allows us to define the Eintein-Hilbert-Palatini action as a measure, which coincides with the Regge action. We apply this alternative formulation of Regge calculus to construct a path-integral measure on histories of the gravitational field and arrive at a spin-foam model of Quantum Gravity. In my talk I will focus on 3D Euclidean gravity.