Carlo Rovelli, University of Pittsburgh

rovelli@phyast.pitt.edu

The canonical quantum gravity community gathered in Warsaw, in June, for the second, but already traditional, Warsaw workshop. A perfect organization, mostly the merit of Jerzy Lewandowski, and a well chosen balance between scientific focus and openings towards nearby areas, have contributed to a dense and exciting meeting. The field is in fibrillation, with excitement, new ideas, and a feel of progress happening; the talks were all packed; and the discussion lively.

By far the largest topic discussed (half of the talks), has been
* loop quantum gravity*. On the side of physical results,
Kirill Krasnov and Abhay Ashtekar reported substantial progress on the
problem of deriving * black hole entropy* from quantum gravity,
developing the earlier works on the subject by Krasnov and Rovelli.
Surprisingly, the long searched derivation of the black hole entropy
formula from quantum gravity has being found, almost simultaneously,
in both the current major approaches to quantum gravity: strings and
loop gravity. The two derivations have opposite strengths and
weaknesses. The string theory one succeeds in computing the precise
entropy/area ratio (), but so far it works only for highly
unphysical (extreme or nearly extreme) holes; while the loop
derivation works for physical cases such as Schwarzschild, but it
does not fix the factor (although it is compatible with
it).

Four talks were devoted to a novel direction in loop quantum gravity:
spacetime covariant versions of the formalism. Mike Reisenberger and
Carlo Rovelli showed how one can derive a sum-over-histories
formulation of loop quantum gravity from the canonical theory,
following earlier ideas by Reisenberger himself and Baez. The
resulting theory has the intriguing form of * a sum over
topologically inequivalent surfaces in spacetime*. Fotini Markopoulou
and Lee Smolin explored Lorentzian versions of this construction.
Covariant formalism do not seem to be an appropriate topic for a
workshop on * canonical* gravity! But maybe old antinomies as
the 4 versus 3+1 views of quantum gravity are finally beginning to
evaporate.

The weak side of loop quantum gravity is the dynamics, still much
debated. Thomas Thiemann, who has recently given a key contribution
by constructing a well-defined hamiltonian operator, described the
extension of his results to the * inclusion of matter*. The
attractive aspect of this new step is that finiteness of the matter
hamiltonian supports the hope that loop quantum gravity could realize
the dream of curing ultraviolet divergences. The discussion on the
physical correctness of the proposed hamiltonian and its variants
focused on the problem of the existence of * anomalies* in the
constraint algebra. Roman Jackiw emphasized the importance of the
problem by discussing some model theories. Don Marolf reported on an
elegant and comprehensive analysis of the constraint algebra by
Lewandowski and himself: The algebra closes in most of the proposed
versions of the hamiltonian constraint. However, it does not seem to
reproduce the classical algebra, and doubts were thus raised on the
physical correctness of the proposed operators.

Other aspects of loop quantum gravity were discussed by Jorge Pullin in a comprehensive review of the state of the Chern-Simon state in the theory, including recent results obtained using the spin-network technology, and by Renate Loll, who introduced a novel technique for the computation of the spectrum of the volume.

The second largest topic discussed, after loop quantum gravity, has
been the problem of formulating quantum mechanics in a form
appropriate for gravity. Jim Hartle reviewed his * generalized
quantum theory* emphasizing its numerous applications. Chris Isham
discussed the formalism of consistent histories, focusing on the
intriguing appearance of * topos theory*, a sophisticated branch
of mathematics, at its roots. The difference in mathematical style
did not hide the fact that these two speakers were talking about the same
formalism. A formalism which has become very relevant for loop quantum
gravity, in view of the recent steps towards spacetime,
sum-over-surfaces
formulations, which fit naturally into the Hartle-Isham quantum
mechanics. Chris left Warsaw before giving his final lecture,
due to an indisposition; but on my way back from Warsaw I had
the fortune of spending a delightful day with him in London, and I
can assure anybody who might have worried that he was again in
perfect conditions!

Ted Newman illustrated the intriguing * reformulation of
general relativity in terms of null surfaces*, recently completed
by himself, Frittelli, Kozameh and others, including applications
to the quantum theory. Mauro Carfora described his analytical
derivation of the existence and location of a critical point in
* simplicial quantum gravity*. Abhay Ashtekar presented
some puzzling ``large'' quantum gravitational effects. Peter
Hajicek discussed the quantization of **2+1** gravity.

Other subjects covered, which I can only list here for lack of space, were quantum field theory on curved spacetime (Fredenhagen); angles (Landsman); relativistic hydrodynamics (Kijowski); exterior gauge fields (Henneaux); dust (Kuchar) and spherical dust shells (Louko); the canonical structure of homogeneous cosmological models (Kodama); the metric representation (Glikman-Kowalski); cylindrical waves quantization (Korotkin); bianchi type VII models (Manojlovic); spinors' evolution (Massarotti); and quantum cosmology (Barvinski).

The workshop was elegantly concluded by an inspiring talk by Jim Hartle, tiled ``Problems for the 21st century'': so that everybody, going home, could know what to do. On another general relativity conference in Warsaw, half a century ago, Feynman wrote a famous comment, not too gentle towards the relativists. Times are gone, and gravity is today a focal point of fundamental physics research. Who knows, had he been there, maybe this time Feynman might have been a bit nicer ...

Wed Sep 10 15:05:58 EDT 1997