Canonical Quantum Gravity-some history/bibliograph

[marcus]

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

 

[marcus]

A passage from Gaul/Rovelli's intro to LQG

towards the end of the preceding post I mentioned Gaul/Rovelli's primer of LQG. It has this interesting description on page 37

"The states |s> are the (3d) diffeomorphism invariant quantum states of the gravitational field. They are labelled by abstract, non-embedded (knotted, colored) graphs s, the s-knots. As we have seen above, each link of the graph can be seen as carrying a
quantum of area. As shown for instance in [34], a similar result holds for the volume: in this case, that are the nodes that carry quanta of volume. Thus, an s-knot can be seen as an elementary quantum excitation of space formed by 'chunks' of space (the nodes) with quantized volume, separated by sheets of surface (corresponding to the links), with quantized area. The key point is that an s-knot does not live on a manifold. The quantized space does [not?] reside 'somewhere'. Instead, it defines the 'where' by itself. This is the picture of quantm space-time that emerges from loop quantum gravity."


Loop Quantum Gravity and the Meaning of
Diffeomorphism Invariance

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

It's a good paper because it spells everything out carefully and explicitly. Follows pretty much the same track as Rovelli/Upadhya
with maybe slightly improved notation. The date is December 1999, so it is a year and a half after Rovelli/Upadhya. Treatment is so close to parallel that one can move over more or less painlessly to the later paper. A bit longer: 52 pages.

 

[R0man]

.

Quantum Gravity and the Loop Approach
http://lanl.arxiv.org/abs/gr-qc/0210094
(Ashtekar)

Bibliography on Loop Quantum Gravity
http://lanl.arxiv.org/abs/gr-qc/0412096
(Sahlmann)

Overall, the history of canonical quantum gravity has been a long and evolving journey, with contributions from numerous researchers and a constant search for new approaches and solutions. The bibliography provided includes some of the key papers that have shaped the field, from early attempts to quantize the metric to the development of loop quantum gravity and the incorporation of matter fields. It also highlights the ongoing research and advancements in the field, such as the application of quantum geometry to cosmology and the study of spin foam models. With each new addition to the bibliography, the understanding of quantum gravity continues to deepen and expand, bringing us closer to a complete understanding of the fundamental nature of the universe.