INTERSECTING CONNES NONCOMMUTATIVE GEOMETRY WITH QUANTUM GRAVITY

JOHANNES AASTRUP, JESPER MØLLER GRIMSTRUP
2007 International Journal of Modern Physics A  
An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. 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 paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a
more » ... spectral triple is outlined and ideas on interpretation and classical limit are presented.
doi:10.1142/s0217751x07035306 fatcat:to5aetrhfre6zbnso2yel33xzy