Spectral triples of holonomy loops

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Original languageEnglish
Pages (from-to)657-681
Number of pages25
JournalCommunications in Mathematical Physics
Volume264
Issue number3
Publication statusPublished - 31 Mar 2006

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 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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Spectral triples of holonomy loops. / Aastrup, Johannes; Grimstrup, Jesper Møller.
In: Communications in Mathematical Physics, Vol. 264, No. 3, 31.03.2006, p. 657-681.

Research output: Contribution to journalArticleResearchpeer review

Aastrup J, Grimstrup JM. Spectral triples of holonomy loops. Communications in Mathematical Physics. 2006 Mar 31;264(3):657-681. doi: 10.1007/s00220-006-1552-5
Aastrup, Johannes ; Grimstrup, Jesper Møller. / Spectral triples of holonomy loops. In: Communications in Mathematical Physics. 2006 ; Vol. 264, No. 3. pp. 657-681.
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