http://arxiv.org/abs/hep-th/0604130(adsbygoogle = window.adsbygoogle || []).push({});

Algebraic approach to quantum gravity II: noncommutative spacetime

S. Majid

26 pages, 2 figures; book chapter to appear in D. Oriti, ed., Cambridge Univ. Press

"We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a thorough account of the bicrossproduct model noncommutative spacetimes of the form [t,x_i]=i lambda x_i and the correct formulation of predictions for it including a variable speed of light. We also study global issues in the Poincaré group in the model with the 2D case as illustration. We show that any off-shell momentum can be boosted to infinite negative energy by a finite Lorentz transformaton."

http://arxiv.org/abs/hep-th/0604132

Algebraic approach to quantum gravity III: noncommmutative Riemannian geometry

S. Majid

25 pages, 1 figure; to appear in collection B. Fauser and J. Tolksdorf, eds., Birkhauser

"This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that arises naturally as the classical limit; a theory with nonsymmetric metric and a skew version of metric compatibilty. Meanwhile, in quantum gravity a key ingredient of our approach is the proposal that the differential structure of spacetime is something that itself must be summed over or 'quantise' as a physical degree of freedom. We illustrate such a scheme for quantum gravity on small finite sets."

==============

remember this connection with QG from earlier this year:

http://arxiv.org/abs/hep-th/0601004

Noncommutative Harmonic Analysis, Sampling Theory and the Duflo Map in 2+1 Quantum Gravity

L. Freidel, S. Majid

54 pages, 2 figs

We show that the *-product for U(su_2) arising in [ref. EL] in an effective theory for the Ponzano-Regge quantum gravity model is compatible with the noncommutative bicovariant differential calculus previously proposed for 2+1 Euclidean quantum gravity using quantum group methods in [ref. BatMa]..."

Freidel is at Perimeter/Lyon and refs are to Freidel-Livine and Majid-Batista.

contact between GFT spinfoam approach and noncommutative geometry.

I do not know what is #1 of this series----we have only paper II and paper III AFAIK

====================

here are the first four refs in the paper Majid has provided as chapter for Oriti book:

[1] G. Amelino-Camelia and S. Majid. Waves on noncommutative space-time and gamma ray bursts. Int. J. Mod. Phys. A 15:4301–4324, 2000.

[2] E. Batista and S. Majid. Noncommutative geometry of angular momentum space U(su2). J. Math. Phys. 44 (2003) 107-137.

[3] L. Freidel and E. R. Livine, “Ponzano-Regge model revisited. III: Feynman diagrams and effective field theory,” hep-th/0502106.

[4] S. Majid and L. Freidel. Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity, hep-th/0601004. [5]

this can help give an idea what Shahn Majid is talking about here and where it fits in.

IMHO dynamite

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# New Majid Algebraic QG papers (Oriti book)

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