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derivation of QED equations of motion from QED Lagrangian ?


Widdekind
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http://en.wikipedia.org/wiki/Quantum_electrodynamics#Equations_of_motion

 

When you take the variational derivative, of the QED Lagrangian, with respect to the wave function [math]\Psi[/math]...

 

why doesn't the derivative include terms, due to the conjugate transpose of the wave function [math]\bar{\Psi}[/math] ?

 

In Classical analogy, for a Lagrangian with the KE term [math]\left( \frac{1}{2m} \vec{p}^T \circ \vec{p} \right)[/math], derivatives with respect to momentum would include (one) terms, from the transpose of momentum, which is essentially the same mathematical object

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