
@reset.
{\alpha,\beta,\gamma}::Indices("spinor").
\dot{#}::Accent.
{\dot{\alpha},\dot{\beta},\dot{\gamma}}::Indices("conjugate spinor").
D{#}::Derivative.
\partial{#}::PartialDerivative.

ddef:= {
   D_{\alpha}{A??} -> \partial_{\alpha}{A??} 
                            + i \sigma^{m}_{\alpha\dot{\alpha}} \theta^{\dot{\alpha}} \partial_{m}{A??},
   D_{\dot{\alpha}}{A??} -> \partial_{\dot{\alpha}}{A??} 
                            + i \theta^{\alpha} \sigma^{m}_{\alpha\dot{\alpha}} \partial_{m}{A??}
};

D_{\alpha}{ D_{\dot{\beta}}{f} } + D_{\dot{\beta}}{ D_{\alpha}{f} };

@substitute!(%)( @(ddef) );


# Example from the Dill paper.
#
@reset.
{\alpha,\beta,\gamma,\delta}::Indices(spinor,type=grassmann,position=fixed).
{\dot{\alpha},\dot{\beta},\dot{\gamma},\dot{\delta}}::Indices(spinor,type=grassmann,position=fixed).
D{#}::Derivative.
{\theta^{\alpha}, \theta_{\alpha}}::SelfAntiCommuting.
{\theta^{\alpha}, \theta_{\beta}}::AntiCommuting.
i::ImaginaryI.


drules:= { D_{\gamma}{A??} -> \partial_{\gamma}{A??} 
                              + i \sigma^{n}_{\alpha\dot{\alpha}} \theta^{\dot{\alpha}} \partial_{m}{A??} 
         };


D_{\gamma}{\theta^{\delta} \theta_{\delta} F};
@prodrule!(%);
