Questions tagged [ward-identity]
The ward-identity tag has no usage guidance.
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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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Ward Identities in Conformal Theory
For a 2D free boson model,
$$
S=\frac{1}{2} g \int d^2 x \; \partial_\mu \varphi\;\partial^\mu \varphi
$$
The energy-momentum tensor should be
$$
T_{\mu \nu}=g\left(\partial_\mu \varphi \partial_\nu \...
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
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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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Ward identity in scalar QED; gauge transformations & plane wave solutions for polarization
I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian:
$$
L = -\frac{1}{4}...
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How should I calculate the commutator between the Belinfante stress tensor and the field operator?
As known, there is an ambiguity on the definition of the stress tensor (or energy-momentum tensor).
The canonical stress tensor, defined as the Noether's current corresponding to space-time ...
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Confusion about the derivation of stress tensor OPE from Ward Identity
I apologize for any difficulty in expressing my review. Allow me to briefly summarize the material and then pose my question.
Review
In David Tong's string lecture note, he derives the OPE between ...
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Three-point function general form
The general matrix element of the electromagnetic current can be written as $$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} + ...
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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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Ward identity of correlation function
For local observables $\{O_i(x_i)\}^n_{i = 1}$, one defines the Ward identity as
$$\partial_{\mu}\langle j^{\mu}(x)\prod^n_{i = 1}O(x_i)\rangle = \sum^n_{i = 1}\delta(x-x_i)\langle O_1(x_1)\cdots\...
user361492
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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 ...
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Contact terms in Schwinger-Dyson equation and Ward-identity
I am reading Weigand's notes for the derivation of Ward-identity.
The Second last paragraph on page 133, says the following statement
"The Schwinger-Dyson equation and the Ward-identity show ...
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