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I am really familiar with the Ward-Takashi identity formulated in the form [itex]k_{\mu}M^{\mu\nu}=0[/itex] applying the fact that the longitudinal polarization of the 4 vector A is nonphysical (redundant) and should not contribute to the physical amplitudes. But, by opening a test subject on QED, I ran into this formula: [itex] -\frac{1}{\alpha}\Box\partial_{\mu}A^{\mu} + \partial^{\mu}\frac{\delta\Gamma}{\delta A^{\mu}} + ie\psi\frac{\delta\Gamma}{\delta\psi} -ie\bar{\psi}\frac{\delta\Gamma}{\delta\bar{\psi}}=0[/itex] which is quite unclear for me. [itex]\Gamma [\psi,\bar{\psi},A][/itex] is the generator of 1PI graphs. Does someone have a reference on the derivation of that, or could show me how to get this?

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# Unclear formulation of Ward identity

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