# The Seiberg-Witten equations for spin 3/2

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Let ${\cal D}^{RS}$ be the Rarita-Schwinger operator and $\tilde \psi=\sum_a \psi^a \otimes e^a$ with an orthonormal basis $(e^a)$ of vectors, $\psi^a$ spinors and $\sum_a e^a \psi^a=0$.

The Seiberg-Witten equations for spin 3/2 are:

$${\cal D}_A^{RS} \tilde \psi=0$$

$$F(A)_+=\omega (\tilde \psi)$$

with

$$\omega (\tilde \psi)= \sum_a <(XY-YX).\psi^a,\psi^a>$$

It doesn't depend on the choice of the basis $(e^a)$.

Is the theory of Seiberg-Witten for the spin 3/2 commutativ?

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