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Tagged with correlation-functionsward-identity
25 questions
3votes
1answer
147views
Ward identity from Ward-Takahashi identity
In Schwartz book Ward-Takahashi and Ward identity are proven in the context of Path Integrals. On page 281 equation (14.150) he use the following Schwinger-Dyson equation for photon: $$ \Box_{\alpha\...
- 776
3votes
0answers
77views
Charge conservation in Scalar QED
I am currently solving problem 14.5 in Schwartz' Quantum Field Theory and the Standard Model. In part (b), Schwartz asks about the difference between the current-conservation Schwinger–Dyson equation ...
- 174
1vote
1answer
104views
Three-point function general form
The general matrix element of the electromagnetic current can be written as $$iM^ {\mu} = \left< p^\prime,s^\prime | j^\mu (x) | p,s\right>=\bar{u}(p^\prime,s^\prime)\left( R(q^2) \gamma^{\mu} + ...
5votes
0answers
164views
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}) &= \...
- 954
3votes
1answer
104views
Confusion regarding time ordering in the Ward Identity derivation
This question does not follow from reading any text, but I was watching Shiraz Minwalla's CFT lectures on YouTube. At 51:36 into the lecture, he raises the question that, as an operator statement, we ...
- 954
2votes
0answers
87views
What are the conformal Ward identities associated with the correlation functions of the stress-energy tensor?
I found two papers on this matter, but am having trouble parsing the answer from either of them. https://arxiv.org/abs/1911.05359 https://arxiv.org/abs/2108.06767 For that matter, what even are the ...
- 1,825
5votes
1answer
617views
Conformal Ward Identity (Di Francesco et al)
In the yellow pages (Conformal Field Theory, Di Francesco, Mathieu, Sénéchal), the authors derive the conformal Ward identity in the following way: They show that, for a conformal transformation, $$ \...
4votes
1answer
499views
Ward-Takahashi Identity in QED
P&S write in Section 7.4 on page 238: We will prove the Ward-Takahashi identity order by order in $\alpha$……The identity is generally not true for individual Feynman diagrams; we must sum over ...
- 1,505
4votes
1answer
952views
Explicit check of Ward identity (Peskin & Schroeder p. 160)
I am trying to check explicitly that the (Compton) amplitude $$i\mathcal{M} = -ie^2\epsilon^*_\mu(k’)\epsilon_\nu(k)\bar u(p’)\left[\frac{\gamma^\mu \not k\gamma^\nu + 2\gamma^\mu p^\nu}{2p\cdot k}+\...
- 709
2votes
0answers
304views
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 ...
- 576
4votes
3answers
187views
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 ...
- 95
7votes
1answer
539views
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 ...
3votes
1answer
579views
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. ...
4votes
2answers
744views
Diffeomorphism Ward identity
I'm trying to prove: (Exercise 2.1. from "TASI Lectures on the Conformal Bootstrap" by David Simmons-Duffin) $$\partial_{\mu} \langle T^{\mu \nu} {\cal O}_{1}(x_{1}) \dots {\cal O}(x_{n}) \...
- 1,337
3votes
1answer
325views
2D CFT correlator involving stress tensor and current
I am recently puzzled by one question in CFT. I want to compute the correlator of $$\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,...
