# Questions tagged [ward-identity]

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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 \begin{equation} q^\mu\Gamma^\mu(p,p')=\Sigma(p)-\Sigma(p') \end{equation} with $q=p-p'$. In the limit $q\rightarrow 0$, \begin{equation} \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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I want to renormalize the minimally-coupled scalar Yang-Mills theory: $$\mathcal{L}_{YM\phi}=(D_\mu\phi)^\dagger(D^\mu\phi)-\frac{1}{4}F_{\mu\nu}^a{F^{\mu\nu}}^a-\frac{1}{2\xi}(\partial_\mu {A^\mu}^a)^... 2 votes 1 answer 182 views ### Am I free to add a contact term to Feynman diagram calculations? In a model with 3 particles \psi, \phi, and \gamma, suppose we have three diagrams and subsequently three amplitudes \mathcal{M}^\mathrm{s}_\mu, \mathcal{M}^\mathrm{t}_\mu and \mathcal{M}^\... 0 votes 1 answer 93 views ### Translation Ward Identity This is a question which wants us to find the variation of the action for the free scalar field under the field transformation \phi(x) \mapsto \phi’(x) = \phi(x) - a(x)\partial_\mu\phi(x) Deduce the ... 4 votes 1 answer 317 views ### How to understand Schwartz chapter19 equation (19.85)? I am reading Schwartz's QFT books, chapter 19. In section 19.5, he claims,in equation 19.85/19.86, that there is a simpler way to prove that Z_1=Z_2 in all orders of perturbation theory. He first ... 3 votes 0 answers 326 views ### Transverse and longitudinal photon propagator I'm studying QED renormalization and the Ward-Takahashi identity, and I'm having trouble understanding two things about the longitudinal and transverse parts of the photon propagator. What I ... 3 votes 1 answer 212 views ### 2D CFT correlator involving stress tensor and current I am recently puzzled by one question in CFT. I want to compute the correlator of$$\langle T(z)J(w)O_1(x_1) O_2(x_2)\rangle$$where T is the stress tensor, J is the U(1) Kac-Moody current, O_1,... 1 vote 1 answer 206 views ### Meaning of \delta A in Ward’s identity in Polchinski In eq (2.3.7) the symbol \delta A(\sigma_0) is introduced in Polchinski:$$ \delta A(\sigma_0)+\frac\epsilon{2\pi i}\int_R d^d\sigma g^{1/2}\nabla_a j^a(\sigma)A(\sigma_0)=0\tag{2.3.7}  but it ...
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I am trying to derive a Ward-type identity between amplitudes involving $\bar\psi \sigma_{\mu\nu}\gamma_5\psi$, $\bar \psi \gamma_\mu \gamma_5 \psi$, and $\bar \psi \gamma_5 \psi$ in QCD (diagonal ...