On Spectral Triples in Quantum Gravity I

Understand

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity.

• A semi-finite spectral triple over a space of connections is presented.
• The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator.
• The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity.