# 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.