Intersecting Connes Noncommutative Geometry with Quantum Gravity

(Joint work with Jesper Grimstrup)

In this talk I will propose an intersection of noncommutative geometry and loop quantum gravity. Alain Connes' noncommutative geometry provides a framework in which the standard model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this talk I will consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. Construction of a spectral triple is outlined and ideas on interpretation and classical limit will be presented.