Computation of the effective action (Peskin 11.4)

babamarysol
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The generating functional Z[J] depends on \phi_{cl} trough its dependence on J. At the lowest order in perturbation theory the relation between J(x) and \phi_{cl} is just the classical field equation:

\left(\frac{\delta L}{\delta \phi}\right)_{\phi=\phi_{cl}} + J(x) = 0

The question is simple: why this expression for the field equation?

Please help me
 
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Ah that's ok it's a functional derivative...
 
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