# Jesper grimstrup

# On Spectral Triples in Quantum Gravity

** Abstract: **

In my talk I will review the construction and interpretation of a
semi-finite spectral triple build from basic ingredients of canonical
quantum gravity. Here, the algebra involves holonomy loops as
functions on a space of connections and the interaction of the Dirac
type operator and the algebra reproduces the structure of the
classical Poisson bracket of General Relativity. Finally, I will show
how semi-classical states which reproduce a classical Dirac operator
are constructed.