Quantizing canonical gravity in the real domain

Abstract

We advocate an alternative description of canonical gravity in 3+1 dimensions, obtained by using as the basic variable a real variant of the usual Ashtekar connection variables on the spatial three-manifold. With this ansatz, no non-trivial reality conditions have to be solved, and the Hamiltonian constraint, though non-polynomial, can be quantized rigorously in a lattice regularization.

4 pages, LaTeX, uses sprocl.sty; to appear in the Proceedings of the 2nd International Sakharov Conference on Physics, Moscow, May 20-24, 1996