I consider a tensor product between the spinor vector bundle and a SU(2) bundle; a Spin-H structure. I take the Dirac operator D_A with a SU(2)-connection A. And next I consider the quaternion SW equations :
F_+ (A)= q(psi)
psi is a quaternion spinor and F_+(A) is the self-dual part of the curvature of the connection A which is an imaginary quaternion.
The moduli spaces are perhaps not compact (Uhlenbeck's lemma?) but perhaps can also be compactified and may give new invariants of four manifolds.