Holonomy Loops, Spectral Triples & Quantum Gravity

A. Ashtekar, “New Variables for Classical and Quantum Gravity,” Phys. Rev. Lett. 57

1986

Earlier work this paper cites.

A. Ashtekar, “New Hamiltonian Formulation of general relativity,” Phys. Rev. D 36

1987

Earlier work this paper cites.

A. Connes, “noncommutative geometry,” Academic Press, 1994

1994

Earlier work this paper cites.

A. Ashtekar and J. Lewandowski, “Differential geometry on the space of connections via graphs and projective limits,” J. Geom. Phys. 17

1995

Earlier work this paper cites.

A. Connes, “Gravity coupled with matter and the foundation of non-commutative geometry,” Commun. Math. Phys. 182

1996

Earlier work this paper cites.

A. H. Chamseddine and A. Connes, “Universal formula for noncommutative geometry actions: Unification of gravity and the standard model,” Phys. Rev. Lett. 77

1996

Cited alongside, same era.

A. H. Chamseddine and A. Connes, “The spectral action principle,” Commun. Math. Phys. 186

1997

Cited alongside, same era.

A. Ashtekar and J. Lewandowski, “Quantum theory of geometry. I: Area operators,” Class. Quant. Grav. 14

1997

Cited alongside, same era.

C. Rovelli, “Quantum gravity,” Cambridge, UK: Univ. Pr. (2004) 455 p

2004

Cited alongside, same era.

A. Ashtekar and J. Lewandowski, “Background independent Quantum Gravity: A status report,” Class. Quant. Grav. 21

2004

Cited alongside, same era.

A. H. Chamseddine and A. Connes, “A universal action formula,” [arXiv:hep-th/9606056]

Cited in the paper.

A. H. Chamseddine, A. Connes and M. Marcolli, “Gravity and the standard model with neutrino mixing,” arXiv:hep-th/0610241

Cited in the paper.

A. H. Chamseddine and A. Connes, “Why the standard model,” arXiv:0706.3688 [hep-th]

Original

Cited in the paper.

A. H. Chamseddine and A. Connes, “A Dress for SM the Beggar,” arXiv:0706.3690 [hep-th]

Original

Cited in the paper.

J. Aastrup, J. M. Grimstrup and R. Nest, “On Spectral Triples in Quantum Gravity I,” arXiv:0802.1783 [hep-th]. To appear in Classical and Quantum Gravity

Original

Cited in the paper.

J. Aastrup, J. M. Grimstrup and R. Nest, “A new spectral triple over a space of connections,” arXiv:0807.3664 [hep-th]. To appear in Communications of Mathematical Physics

Original

Cited in the paper.

T. Thiemann, “Introduction to modern canonical quantum general relativity,” [arXiv:gr-qc/0110034]

Cited in the paper.

J. Aastrup and J. M. Grimstrup, “Spectral triples of holonomy loops,” Commun. Math. Phys. 264

2006

Later among the works it cites.

J. Aastrup and J. M. Grimstrup, “Intersecting Connes noncommutative geometry with quantum gravity,” Int. J. Mod. Phys. A 22

2007

Later among the works it cites.

J. Aastrup, J. M. Grimstrup and R. Nest, “On Spectral Triples in Quantum Gravity II,” arXiv:0802.1784 [hep-th]. J. Noncommut. Geom

Original

2009

Closest in time.

A. Connes, ”On the spectral characterization of manifolds” [arXiv:0810.2088]

Original

2088

Closest in time.