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arXiv · hep-th/0503246

Spectral triples of holonomy loops

Johannes Aastrup·Jesper M. Grimstrup
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Abstract

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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Johannes Aastrup, Jesper M. Grimstrup. 2006-01-18. Spectral triples of holonomy loops. https://doi.org/10.1007/s00220-006-1552-5

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