I am reading the Taubes's paper: From From Seiberg Witten to pseudo-holomorphic curve. I don't know how to get the result (2.17)
\begin{eqnarray*} &&dd^*(\frac{r}{8}(1-|\alpha|^2+|\beta|^2)\omega-\frac{r}{4}(\alpha^*\beta+\alpha\beta^*))\\ &=&\frac{r}{4}iF_a(|\alpha|^2+|\beta|^2)+\frac{ir}{4}(\nabla_a\alpha^*\wedge\nabla_a\alpha + \nabla_A\beta^* \wedge \nabla_A\beta )\\ &&-\frac{ir}{8}d(\alpha\beta^*k- \alpha^*\beta k^* )+\frac{r}{4}ik|\beta|^2 \end{eqnarray*}
Moreover, the computation (2.16) make me confuse.... Can someone give me the computational process??