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We have had some discussion of this in earlier threads.

Alain Connes et al have been able to derive the standard menu of particles from a certain spectral triple, in Noncommutative Geometry (NCG).

On the other hand, Loop Quantum Gravity (LQG) as developed by Rovelli, Smolin and many others is primarily a quantum theory of spacetime geometry---thus it contains gravity but not the matter fields of the standard particle model.

For over two years now, Johannes Aastrup and Jesper Grimstrup have been investigating a way of combining NCG with LQG, so that LQG would not only constitute a quantized version of General Relativity---a quantum theory of gravity, in other words----but would also contain the Standard Model. It is an approach to unification.

The two original researchers have been joined by a third, Ryszard Nest. Now Aastrup, Grimstrup and Nest have brought out two new papers as part of this program:

http://arxiv.org/abs/0802.1783

Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest

84 pages, 8 figures

(Submitted on 13 Feb 2008)

"This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject."http://arxiv.org/abs/0802.1784

Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest

43 pages, 1 figure

(Submitted on 13 Feb 2008)

"A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject."

Alain Connes et al have been able to derive the standard menu of particles from a certain spectral triple, in Noncommutative Geometry (NCG).

On the other hand, Loop Quantum Gravity (LQG) as developed by Rovelli, Smolin and many others is primarily a quantum theory of spacetime geometry---thus it contains gravity but not the matter fields of the standard particle model.

For over two years now, Johannes Aastrup and Jesper Grimstrup have been investigating a way of combining NCG with LQG, so that LQG would not only constitute a quantized version of General Relativity---a quantum theory of gravity, in other words----but would also contain the Standard Model. It is an approach to unification.

The two original researchers have been joined by a third, Ryszard Nest. Now Aastrup, Grimstrup and Nest have brought out two new papers as part of this program:

http://arxiv.org/abs/0802.1783

**On Spectral Triples in Quantum Gravity I**Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest

84 pages, 8 figures

(Submitted on 13 Feb 2008)

"This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of General Relativity. Moreover, the associated Hilbert space corresponds, up to a discrete symmetry group, to the Hilbert space of diffeomorphism invariant states known from Loop Quantum Gravity. Correspondingly, the square of the Dirac operator has, in terms of canonical quantum gravity, the form of a global area-squared operator. Furthermore, the spectral action resembles a partition function of Quantum Gravity. The construction is background independent and is based on an inductive system of triangulations. This paper is the first of two papers on the subject."http://arxiv.org/abs/0802.1784

**On Spectral Triples in Quantum Gravity II**Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest

43 pages, 1 figure

(Submitted on 13 Feb 2008)

"A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject."

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