Abhay Ashtekar, Penn State

ashtekar@phys.psu.edu

A 2-month workshop was held at the Erwin Schrödinger International Institute for Mathematical Sciences in Vienna during July and August, '96. It was jointly organized by Peter Aichelburg and myself.

There were 23 participants from outside Austria, mostly young physicists who have been working on various aspects of quantum gravity. In addition, about a dozen faculty and students from Vienna actively participated in the seminars and discussions. While the focus of this effort was on non-perturbative quantum general relativity, there were several experts from string theory, supergravity, quantum cosmology, quantum field theory, as well as mathematical physics in a broad sense of the term. Unfortunately, there was a rather severe desk-space limitation in July and so the workshop had to make do without the participation of a number of experts who had time-constraints of their own. There were two weekly ``official seminars" which were widely announced --one entitled ``fundamental issues", and the other ``advanced topics". They enhanced the scientific interaction between workshop participants and the local physics and mathematics community. In addition, there were ``discussion seminars" (the remaining) three days a week. The afternoons were left open for further informal discussions (and real work!).

On the scientific front, the workshop elevated the subject to a new
level of maturity. It enabled the participants to take stock of a
number of areas to obtain a global picture of issues that are now
well-understood and also opened new directions for several other key
issues. Because of the space limitation, I will restrict myself here
only to a few illustrative highlights. A more detailed discussion of
the (July) activities can be found in John Baez's ``This Week's Finds"
series, weeks 85-88 (
` http://math.ucr.edu/home/baez/twf.html`) which
also contains many references. A Schrödinger Institute pre-print
containing abstracts of seminars will be available early
October. Further information on the workshop as well as pre-prints of
research carried out during the workshop can be obtained from the
Schrödinger Institute home page
` http://www.esi.ac.at/ESI-Preprints.html`).

In the list that follows, the names in parenthesis refer to people who gave seminars or led discussions (although almost everyone present made significant contributions to all the discussions).

* Quantum Hamiltonian constraint.* (Hans-Jürgen Matschull,
Jorge Pullin, Carlo Rovelli, Thomas Thiemann)

* Quantum geometry.* (AA, Jerzy Lewandowksi, Renate Loll,
Thiemann)

* Lattice methods and skeletonization in loop quantum gravity.*
(Loll, Michael Reisenberger)

* Super-selection rules in quantum gravity.* (AA, Lewandowski,
Donald Marolf, Jose Mourão, Thiemann)

* Degenerate metrics: extensions of GR.* (Ted Jacobson,
Lewandowski, Matschull)

* Global issues, Hamiltonian formulations.* (Fernanado Barbero,
Domenico Giulini)

* Mathematical issues in quantum field theory and quantum
gravity.* (John Baez, Matthias Blau, Herbert Balasin, Rodolfo
Gambini, Mourao, Marolf)

* Exactly soluble midisuperspaces.* (AA, Hermann Nicolai)

* Lessons from low dimensional gravity.* (AA, Giulini,
Lewandowski, Marolf, Mourao, Thiemann, Strobl).

* Black-hole entropy.* (Jacobson, Kirill Krasnov, Marolf,
Rob Myers, Rovelli)

* Topological quantum field theories* (Baez, Reisenberger)

* String duality, conformal field theories* (Jürgen Fuchs,
Krzysztof Meissner, Myers, Strobl)

* Foundations of quantum mechanics and quantum cosmology*
(AA, Giulini, Jonathan Halliwell, Franz Embacher)

If participants were to single out one topic that generated most
excitement, it would probably be the regularization of the Hamiltonian
constraint by Thiemann
(gr-qc/9606088,
89,
90,
91). This has significantly deepened our
understanding of the mathematical problems underlying quantum dynamics
of general relativity. (For details, see Baez's article in this
issue.) However, a number of important problems remain. In
particular, during the workshop it was realized that these regularized
quantum constraints have the feature that they strongly commute not
only on diffeomorphism invariant states (which is to be expected
physically) but also on a rather large class of states which are not
diffeomorphism invariant (which is alarming from a physical
viewpoint). A related potential difficulty is with the semi-classical
limit: it is not clear if all the quantum constraints, taken together,
admit a sufficient number of semi-classical states. Analogous
calculations in 2+1 dimensions indicate that the appropriate
semi-classical sector * does* exist. In 3+1 dimensions, further
work is needed. This will no doubt be an area of much research and new
effort in the coming year.

Sun Sep 1 16:45:26 EDT 1996