Spectral triples of holonomy loops

Details Spectral triples of holonomy loops Spectral triples of holonomy loops

2005-03-31

arxiv.org/abs/hep-th/0503246v2

Commun.Math.Phys. 264 (2006) 657-681

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, material added, references added, version accepted for publication in Communications in Mathematical Physics

Scientific paper

10.1007/s00220-006-1552-5

The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of Lie-groups composed of copies of the gauge group. A spectral triple over the space of connections is obtained by factoring out the diffeomorphism group. The triple consist of equivalence classes of loops acting on a separable hilbert space of sections in an infinite dimensional Clifford bundle. We find that the Dirac operator acting on this hilbert space does not fully comply with the axioms of a spectral triple.

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