Jesper Grimstrup

On Spectral Triples of Holonomy Loops


In my talk I will show how a semifinite spectral triple is obtained from a rearrangement of central elements of Loop Quantum Gravity. The triple is based on a countable set of graphs and the algebra consists of holonomy loops in this set. The Dirac type operator resembles a global functional derivation operator. The interaction between the algebra of holonomy loops and the Dirac type operator reproduces the structure of the Poisson bracket of General Relativity. In the talk I will argue how one might obtain a Hamilton constraint from the spectral triple construction.