ORIGIN OF ASHTEKAR VARIABLES IN A PURE-CONNECTION THEORY OF GRAVITY

A pure-connection formulation of general relativity is presented in wh ich the only dynamical variable present in the action is a connection one-form with values in the Lie algebra of the pseudounitary group SU( 2,2). The action is quadratic in the curvature and is independent of a ny space-time metric. Although manifestly SU(2,2) gauge invariant, the symmetry group of the action can be broken down to that of the Lorent z group SL(2,C) yielding Jacobson and Smolin's covariant self-dual ver sion (module a topological and cosmological term) of the Ashtekar form ulation of general relativity.