SELF-DUAL YANG-MILLS FIELDS AND ASHTEKAR VARIABLES

In the phase space of a complex SO(3) Yang-Mills theory, one may define the Yang-Mills Hamiltonian HYM, which gives Yang-Mills theory, and Ashtekar's constraints, which give general relativity. The author looks for points on Ashtekar's constraint surface which stay on that surface under the evolution generated by HYM. Such points exist for non-zero values of the cosmological constant; in general relativity, they correspond to self-dual spacetimes and, in Yang-Mills theory, to Yang-Mills fields which are self-dual with respect to a metric constructed algebraically from the Yang-Mills electric field.