AN ACTION PRINCIPLE FOR SELF-DUAL YANG-MILLS AND EINSTEIN EQUATIONS

We propose actions from which the self-dual Yang-Mills and Einstein equations in four dimensions follow by straightforward variation. This off-shell formulation essentially involves harmonic variables. After reformulation in harmonic space, the self-duality constraints can be derived from actions with the help of Lagrange multipliers. The latter turn out not to describe additional degrees of freedom. The off-shell theories obtained can be quantized in a standard way.