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A short overview of quantum geometry by Ashtekar (2002)

http://www.arxiv.org/abs/math-ph/0202008

A recent paper by Perez (2003) points out that quantum geometry, or Loop Quantum Gravity as it is often called, incorporates matter fields in a divergence-free way without the need for the usual renormalizations to remove infinities. As Thiemann discovered, the infinities do not arise essentially because volumes are quantiized.

See page 4 of Perez

http://lanl.arxiv.org/abs/gr-qc/0301113

and the reference to previous work by Thiemann (1997)

http://arxiv.org/abs/gr-qc/9705019

The incorporation of fermions by LQG, in particular, has recently proven essential. Corichi confirmed the theory's SU(2) symmetry by invoking (local) fermion number conservation consistent with the Immirzi constant being 1/8.088 See Corichi(2002)

http://lanl.arxiv.org/abs/gr-qc/0212126

Quantum Cosmology

A recent paper by Ashtekar on Loop Quantum Cosmology shows that the time-zero singularity does not arise in the LQG model of the big bang. The model incorporates matter in an essential way and shows that the extreme conditions at time-zero nevertheless remain bounded. See Astekar et al (2002)

http://www.arxiv.org/abs/gr-qc/0304074

http://www.arxiv.org/abs/math-ph/0202008

A recent paper by Perez (2003) points out that quantum geometry, or Loop Quantum Gravity as it is often called, incorporates matter fields in a divergence-free way without the need for the usual renormalizations to remove infinities. As Thiemann discovered, the infinities do not arise essentially because volumes are quantiized.

See page 4 of Perez

http://lanl.arxiv.org/abs/gr-qc/0301113

and the reference to previous work by Thiemann (1997)

http://arxiv.org/abs/gr-qc/9705019

The incorporation of fermions by LQG, in particular, has recently proven essential. Corichi confirmed the theory's SU(2) symmetry by invoking (local) fermion number conservation consistent with the Immirzi constant being 1/8.088 See Corichi(2002)

http://lanl.arxiv.org/abs/gr-qc/0212126

Quantum Cosmology

A recent paper by Ashtekar on Loop Quantum Cosmology shows that the time-zero singularity does not arise in the LQG model of the big bang. The model incorporates matter in an essential way and shows that the extreme conditions at time-zero nevertheless remain bounded. See Astekar et al (2002)

http://www.arxiv.org/abs/gr-qc/0304074

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