where is the Dirac operator , is the Covariant Derivative onSpinors, is the Curvature Scalar, and is the self-dual part of the curvature of .See also Lichnerowicz-Weitzenbock Formula
References
Donaldson, S. K. ``The Seiberg-Witten Equations and 4-Manifold Topology.'' Bull. Amer. Math. Soc.33, 45-70, 1996.