I want to be able to treat $ z$ and its complex conjugate as independent variables, so that for instance $ \partial (z\bar z)/\partial z = \bar z$ . When I try to do this in Mathematica, via
D[z Conjugate[z], z]
it returns $ z1$ Conjugate$ ^\prime(z1)+z1^*$ , because it treats $ \bar z$ as if it is a function of $ z$ (which of course it is).
Is there a clever way to tell Mathematical that $ z$ and $ \bar z$ should be treated as independent when evaluating derivatives? Or would the best option be just to use two explicitly independent variables $ z,w$ and later substitute $ w=\bar z$ ?
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