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INTERSECTING CONNES NONCOMMUTATIVE GEOMETRY WITH QUANTUM GRAVITY

JOHANNES AASTRUP

Institut für Analysis, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

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and

JESPER MØLLER GRIMSTRUP

NORDITA, Blegdamsvej 17, DK-2100 Copenhagen, Denmark

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https://doi.org/10.1142/S0217751X07035306Cited by:16 (Source: Crossref)

Abstract

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 spectral triple is outlined and ideas on interpretation and classical limit are presented.

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