About Ward Identity

  • Thread starter myqphy
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This is a question about Ward-Takahashi Identity.I go through the materials presented about Ward Identity in Peskin's book. there are two sections where mentioned this identity. First, in section 5.5, when the author discussed photon polarization sums. Second, in section7.4, where the author present a proof of Ward identity based on Feynman diagram.

Accroding to the methodology the author used. it seems that the discussion based on the classical theorem of current conservation is somehow "cheating" (see the first paragraph of chapter 7), for in section 5.5, they just supposed that the current conservation can be directly extended to quantum case. Although it is somehow cheating, we can clearly see the connection between Ward identity, current conservation and more important, gauge invariance.

Quite contrary, from the derivation which is not"cheating" in section 7.4. I can not clearly see the connection between gauge invariance and current conservation. Even more, by using the methodology of the author, it seems that Proca field(if we assume there is minmum coupling between Proca field and Dirac field), which is not gauge invariant, still obeys the Ward Identity. So I was totally confused of it.

So my question is, how can I find the connection between gauge invariance and Ward Identity from the derivation in section 7.7?

Than you very much

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