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Jesper Grimstrup
On Spectral Triples of Holonomy Loops
Abstract:
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.