Jeanette E. Nelson Dipartimento di Fisica Teorica Universita` di Torino Via P. Giuria 1 -10125 Torino Tel. +39-011-670-7207,Fax+39-011-670-7214 E-mail: nelson[A]to.infn.it

Quantum Gravity Research

The quantisation of the gravitational field remains a great challenge for theoretical physics despite over seventy years of research. The problems are essentially of two types - those of a conceptual nature and those more technical. The main technical problem is that the perturbative approach (splitting the field potential, usually the metric tensor, in a flat, zero curvature part, and a first order deviation from flatness) is non - renormalisable, with the result that one does not know to calculate scattering cross-sections. The conceptual problems include, for example, the choice of time variable, possible alternatives to the Einstein-Hilbert action, which variables to quantise, ordering problems of quantum operators, the interpretation of Einstein's equations (e.g. as operators which should project out physical states, or as identities) etc. Perturbative techniques are not necessary for discussing these problems.

Since 1974 I have worked in non-perturbative Quantum Gravity, firstly on a spinor cosmological model (my Ph.D. thesis) and then on arbitrary spinor-gravitational couplings. I studied first-order and 'new variables' formulations, and then, in 1989, started to study 2+1 dimensional gravity. I still work in this field, though I have changed my approach several times.

I have collaborated with Isham, Bunster (Teitelboim), Charap, Henneaux, Regge, Carlip, Moncrief, Chekhov and Picken. My publications