Details
| Original language | English |
|---|---|
| Pages (from-to) | 657-681 |
| Number of pages | 25 |
| Journal | Communications in Mathematical Physics |
| Volume | 264 |
| Issue number | 3 |
| Publication status | Published - 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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Communications in Mathematical Physics, Vol. 264, No. 3, 31.03.2006, p. 657-681.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Spectral triples of holonomy loops
AU - Aastrup, Johannes
AU - Grimstrup, Jesper Møller
PY - 2006/3/31
Y1 - 2006/3/31
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33646536604&partnerID=8YFLogxK
U2 - 10.1007/s00220-006-1552-5
DO - 10.1007/s00220-006-1552-5
M3 - Article
AN - SCOPUS:33646536604
VL - 264
SP - 657
EP - 681
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 3
ER -