The Seiberg-Witten equations for forms

Question

Let $(M,g)$ be a riemannian manifold of 4 dimension. Let $ a\in \Lambda_+$ and $b\in \Lambda^1$. The Seiberg-Witten equations for forms are: $$da+b\wedge a=0$$ $$db_+=\frac{a}{||a||}$$ The gauge group acts : $$f.(a,b)=(fa,b-df/f)$$ Can we define invariants?

Comments

can you correct the notation for a successful compilation?

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Sorry, but presently I am not able to edit my own question.