# Questions tagged [ward-identity]

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### Ward identity for special conformal transformation in d dimensions

I am reading CFT from the yellow book ( "Conformal Field Theory" by Francesco, Mathieu, Sénéchal ). In section 4.3.2, they calculate three Ward identities corresponding to (i) translation ...
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### $Z_1=Z_2$ and its relation to vertex renormalization in QED

I have been working on the full renormalization of scalar QED with self-interactions, following the steps of Schwartz’s treatment on spinor QED (Chap 19). I have 3 main questions regarding this: Need ...
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### Renormalization in Background field gauge

The purpose of this question is not very straightforward to explain. So, I just state the question. If we use Background field gauge for renormalization, due to the QED-like Ward identities, the ...
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### N=4 Supersymmetric Ward identity

(This question pertains to exercise 4.13 of Elvang and Huang's textbook (which used to be lecture notes). This is not for a class, just to learn some new tools for work). Consider the expansion of the ...
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### Derivation of the Conformal Ward Identity in Di Francesco et al

I am reading section 5.2.2. (titled The Conformal Ward Identity) from Conformal Field Theory by Di Francesco et al. The authors write \begin{align} \partial_\mu(\epsilon_\nu T^{\mu\nu}) &= \...
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### Consequences for symmetries of the equations of motion in QFT

In general, if a Quantum Field Theory is described by a Lagrangian $\mathcal{L}$, the symmetries of $\mathcal{L}$ lead to classically conserved currents along the equations of motion and Ward ...
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### Charge renormalization using Ward identity

In Mandl & Shaw's Quantum Field Theory (p 181), the Ward identity $$\frac{d\Sigma(p)}{dp_\mu} = \Lambda^\mu(p,p)\tag{9.60}$$ where $\Sigma(p)$ and $\Lambda^\mu (p^\prime,p)$ are respectively the ...
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### Gauge invariance and Ward Identity?

I have to work on vacuum polarization and gauge contributions for a given problem. I have to compute and show that their sum is gauge invariant, which according to the exercise, is equivalent to ...
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### Diagrammatic Ward Identity for the QED vertex

The QED Ward identity for the vertex reads $$q^\mu\Gamma^\mu(p,p')=\Sigma(p)-\Sigma(p')$$ with $q=p-p'$. In the limit $q\rightarrow 0$, \Gamma^\mu(p,p)=\...
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### Faddeev-Popov trick in QED Peskin and Schroeder

On page 297 of Peskin and Schroeder, the book obtains the propogator $$\tag{9.58} \tilde{D}_F^{\mu\nu}(k)=\frac{-i}{k^2+i\epsilon}\bigg(g^{\mu\nu}-(1-\xi)\frac{k^\mu k^\nu}{k^2}\bigg).$$ The book then ...
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### Does the Ward-Takahashi identity work for a virtual photon?

In the reaction of the transformation of an electron pair into a muon pair is performed Ward–Takahashi identity. Why if there is no interaction with a real photon?
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### Unphysical gauge boson polarizations in non-abelian gauge theory

I am learning P&S's chapter 16 , quantization of non-abelian gauge theory.(all my ref. formula in this post lie in P&S's book) I am puzzled for the logic of the unphysical polarization of ...
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### Do Ward identities imply that there is an (effective) Lagrangian invariant under the symmetry?

In usual perturbative QFT, if the UV Lagrangian is invariant under a symmetry $G$ and the regularization of the path integral does not break $G$, the Feynman rules are explicitly invariant under $G$. ...
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### Ward-Takahashi Identity in QED

P&S write in Section 7.4 on page 238: We will prove the Ward-Takahashi identity order by order in $\alpha$……The identity is generally not true for individual Feynman diagrams; we must sum over ...
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### Conformal Ward identity minus sign error

I'm trying to track down what seems like a fairly crucial minus-sign error in Di Francesco et al's conformal field theory book. The minus sign has to do with the Ward identity for Lorentz ...
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### Symmetric stress-energy tensor in CFT

I'm a bit confused reading about the stress-energy tensor and conformal Ward identities in Di Francesco. My question is in a similar spirit to this one from several years ago, but the question was not ...
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### On-shell propagator to an off-shell propagator

I am learning the Ward-Takahashi Identity part of Peskin and Schroeder's textbook of quantum field theory. In the prove process, it involves a diagram 7.66. Then it says that I can understand ...
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### PCAC - Ward Identity for non-conserved currents - Derivative and $T$-Order Commutation

I'm currently studying Goldberger-Treiman relation from the book by S. Coleman (Aspects of Symmetry, chapter 2) in which, working in the framework of a not better precised "weak interaction ...
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### Why the matrix element grows with energy in this case?

Consider the QED with massive photons: $$\mathcal{L} = g\bar{\psi}\gamma^{\mu}\psi A_{\mu}, \quad g = \text{const}$$ Because of the current conservation, the contribution of the longitudinal ...
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### Conformal Ward identities for local conformal algebra: error in textbook?

In Schottenloher's mathematically-oriented CFT textbook, "A Mathematical Introduction to Conformal Field Theory," Proposition 9.8 on page 160 states the conformal Ward identities for 2D CFTs ...
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### Is gauge invariance necessary to have Ward identity hold for off-shell amplitudes?

In this other SE post: Is it really proper to say Ward identity is a consequence of gauge invariance? it is shown that the on-shell Ward identity is a consequence of global $U(1)$ symmetry for QED. ...
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### A Question about Conformal Invariance in String Theory

I've been revisiting my lecture notes on string theory. There's one question about conformal invariance suddenly popped up in my head which made me very confused. Starting from Polyakov action S[X,g]...
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