During two weeks in November and December 2002, approximately 20 researchers in quantum gravity gathered at the Raman Research Institute in Bangalore for an intensive meeting on Loop Quantum Gravity and related issues. Talks were divided into morning sessions, shared by Abhay Ashtekar and Martin Bojowald, and afternoon sessions for the rest of the participants.
Abhay Ashtekar gave quite a detailed overview of three main topics: Quantum geometry, black hole entropy, and semi-classical issues. After an introductory talk to set the stage of his series of lectures and a discussion on the quantum mechanics on SU(2), he gave two talks about connections on graphs and field theories of connections, both from the classical and the quantum perspective. They were followed by a lecture devoted to quantum Riemannian geometry and the definition of area and volume operators. After his introduction on quantum geometry he talked about the quantum geometry of isolated horizons and black hole entropy; he discussed, in particular, new results on the computations of entropy for non-minimally coupled scalar fields. Finally his three last talks were devoted to the discussion of semi-classical issues. In the first he used the quantum mechanics of a particle to study how the polymer-like quantum theory of a particle reduces to the usual Schrödinger Quantum Mechanics in the low energy regime. He then considered Maxwell theory in the next lecture, complementing a previous discussion of Madhavan Varadarajan's first talk and finished with an enlightening lecture on the relationship between the Fock, r-Fock, and polymer representations of Maxwell theory. On Dec, 4th he gave a public Academy Lecture on loop quantum gravity in front of a full auditorium. The ten one-and-a-half hour talks succeeded in providing an introduction to the main topics for non-experts and yet gave an insightful review of the present state of loop gravity and its applications. The talks sparked a lot of interaction among the participants in coffee breaks and informal discussion sessions and gave a clear idea of the status of the program and its future development. In spite of a winter cold Abhay displayed a lot of enthusiasm and energy that were certainly inspiring for the rest of the participants.
Martin Bojowald's talks we devoted to the mathematical issues related to symmetry reductions of theories of connections and their application to the study of loop quantum cosmology. He devoted his first three talks to the discussion of the mathematics of symmetry reductions for theories of connections and the definition of symmetric states in quantum geometry. After that he gave a thorough introduction to the kinematics of cosmological models, matter Hamiltonians, quantization ambiguities, and the study of homogenous and isotropic models. He discussed several cosmological issues from the loop quantum gravity perspective; in particular he gave a detailed overview of the meaning of the initial singularity and initial conditions, evolution through classical singularities, large volume behavior and corrections to the classical approach to singularities. He also discussed the possibility of explaining inflation within his framework. It was really impressive to see how far the developments on loop quantum cosmology have reached and the impulse that Martin's work is giving to the whole loop quantum gravity program.
Afternoon sessions covered a much broader set of topics on classical and quantum gravity, cosmology, and quantum field theory. Talks were shorter and were given by a number of speakers. Sukanya Sinha reviewed the approach to the semiclassical Einstein equations pioneered by Bei Lok Hu and to which she has made recent contributions. P. Majumdar discussed some aspects related to the computation of quantum corrections to black hole entropy, in particular he discussed computations for BTZ and AdS-Schwarzschild black holes. L. Sriramkumar gave two introductory talks discussing some issues related to inflation and quantum gravity. T. R. Govindarajan gave us a talk about recent developments in de Sitter gravity, specifically on the thermodynamics of the cosmological horizon of the de Sitter space-time. J. Samuel discussed a novel proposal to test general relativity by using radio interferometers with intercontinental baselines and measuring the curvature of the wavefront emitted by a distant source. G. Date gave a talk on a recent model of his to describe discrete time evolution in a simple quantum mechanical system that mimics some of the features of the symmetric cosmological models discussed by Bojowald. Madhavan Varadarajan gave several talks about his last work on quantum linearized gravity and the r-Fock representation, in particular the use of U(1) flux nets in the context of the simple model provided by electromagnetism. Finally, the author of these lines discussed his work on diff-invariant and non diff-invariant free actions and their use in perturbative quantum gravity.
The meeting was very successful in all the possible aspects. The talks were interesting and illuminating with a lot of discussion during and after the seminars. The atmosphere among the participants was excellent and the scientific exchange really fruitful. I would like to emphasize the perfect organization of the meeting by Madhavan and the very warm hospitality of the whole theory group at RRI. I believe that all the participants are looking forward to attending future meetings at the Raman Institute.