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marcus

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**Quantum Gravity--some history/bibliography**

The inclusion of matter fields

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

(Thiemann: quantum gravity as regulator of matter fields)

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

(Corichi: fermion conservation invoked to show the Immirzi constant 1/8.088 is consistent with SU(2) symmetry)

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

(Perez: divergence-free incorporation of matter, page 4)

Determining the Immirzi parameter

http://www.arxiv.org/abs/gr-qc/9710007

(Ashtekar Baez Corichi Krasnov)

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

(Corichi)

Short overview, ideas not formulas

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

(Ashtekar)

Primer

http://lanl.arxiv.org/abs/gr-qc/9910079

(Gaul/Rovelli)

Quantum Cosmology

http://www.arxiv.org/abs/gr-qc/0304074 (Ashtekar et al.)

Spin Foam

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

(Perez)

History

R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).

That same year, 1962, saw the publication of Wheeler's

book "Geometrodynamics".

The Wheeler-De Witt equation also called the "Quantum-Einstein Equation" De Witt's papers are dated around 1967.

Attempts to construct a quantization of the ADM version of General Relativity appear to go back to the Sixties or possibly earlier.

The first attempts quantized the metric and this approach met with a major roadblock which is what motivated Ashtekar to look for new variables. In 1986 Ashtekar reformulated General Relativity in terms of the connection---- "connection-dynamics" as distinct from Wheeler's "geometrodynamics". And loops emerged as the basic functions defined on connections, i.e. the basis for defining quantum states. But it was still the same program----the geometry was embodied by the connection instead of in the metric, and the states by loops, but the goal was the same: quantum geometry.

So after 1986 the configuration space was the space of all possible connections on the manifold and quantum states Ψ

were functions defined on that space---functions of connections.

Rovelli's LivingReviews article gives some of the main dates:

Ashtekar has a good recent overview, Quantum Geometry in Action

arXiv:math-ph/0202008

that describes among other things work by Martin Bojowald

in Quantum Cosmology---applying quantum geometry to the big bang to give a straightforward resolution of the cosmological singularity.

In the unquantized form the curvature goes to infinity as you move back towards "time zero" and

Bojowald constructed the corresponding quantum picture and looked at the curvature

*operator*and discovered that it is bounded----the quantum curvature does not go to infinity. resolves the singularity.

The shortest summary of LQG still seems to be the socalled "primer" written by Rovelli and Upadhya

arXiv:gr-qc/9806079

Thiemann's massive LivingReview article is called

"Introduction to Modern Canonical Quantum General Relativity"

by "modern" he means the loop approach (since 1986) as distinguished from the earlier (1962-1986) metric-based approach

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