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Unclear formulation of Ward identity

  1. Jan 14, 2012 #1
    Hello,

    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?
     
  2. jcsd
  3. Jan 14, 2012 #2
    Section 12.1, eq. 12.13 in Kaku "Quantum Field Theory - A modern introduction" (1993)
     
  4. Jan 15, 2012 #3
    Thanks, I checked in Kaku's book, and indeed it's not hard to derive, by playing with [itex]Z[\eta,\bar{\eta},J^{\mu}][/itex] and [itex]\Gamma[\psi,\bar{\psi},A^{\mu}][/itex].
     
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