In QED, according to Schwinger-Dyson equation,
(ημν(∂2)−(1−1ξ)∂μ∂ν)⟨0|TAν(x)...|0⟩=e⟨0|Tjμ(x)...|0⟩+contact terms
And the term
(ημν(∂2)−(1−1ξ)∂μ∂ν) is just the inverse bare photon propagator, so if we put the photon on shell, then the l.h.s will yield the complete n-point Green function with the complete photon propagator removed and also multiplied by a factor
Z3, the vector field renormalization constant.
But the r.h.s gives
∂μ⟨0|Tjμ(x)...|0⟩=contact terms
which is the common complete (n-1)-point complete Green function.
So if we truncate all the n-1 external complete propagators, then we are left with the proper vertex Ward identity.
The problem is, now the constant Z3 appeared.
But the well known Ward identity, e.g.
pμΓμP(k,l)=H(p2)[iS−1(k)−iS−1(l)]
doesn't contain
Z3.
Where went wrong? Please help.
This post imported from StackExchange Physics at 2014-09-30 06:47 (UTC), posted by SE-user LYg