Jesper grimstrup

On Spectral Triples in Quantum Gravity


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.