Questions tagged [ward-identity]
162 questions
40
votes
3 answers
Is it really proper to say Ward identity is a consequence of gauge invariance?
Many (if not all) of the materials I've read claim Ward identity is a consequence of gauge invariance of the theory, while actually their derivations only make use of current conservation $\partial_\mu J^\mu=0$ (which is only equivalent to a global…
Jia Yiyang
- 4,135
18
votes
1 answer
How does the Ward-Takahashi Identity imply that non-transverse photons are unphysical in QED?
Peskin and Schroeder say that the Ward Identity of QED proves that non-transverse photon polarizations can be consistently ignored, but I'm confused about the details.
Setup
One starts by considering some process with an external photon whose…
user26866
- 3,582
- 26
- 37
16
votes
1 answer
QED and anomaly
I've just started to learn anomalies in quantum field theories. I have a question.
How to show that QED is free from vector current anomaly and what would happen if it were not? In other words, how can we show that $\partial_\mu j^\mu=0$ even at…
SRS
- 27,790
- 13
- 115
- 365
15
votes
1 answer
Why can I replace a gauge field $A^{\mu}$ by the current $j^{\mu}$ it couples to in the calculation of a Greens function?
I am reading about anomalies in QFT at the moment and have a related question.
Often people calculate the time ordered expectation value of some fields (in QED for example) by replacing the field $A_\mu$ with the current $j_\mu =…
user9784
- 481
12
votes
2 answers
Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory
Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument:
... With a generalization of the argument given there (section 7.4 for Ward identity), on can show that the…
LYg
- 1,201
11
votes
0 answers
gauge invariance of the Feynman amplitudes
When we calculate the photon polarization sums over amplitudes,
$$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$
we find it very helpful that we can simply make a…
LYg
- 1,201
11
votes
2 answers
Ward identity derived from global symmetry and SDE, different from that derived from gauge symmetry?
In QED, according to Schwinger-Dyson equation $^{[1]}$,
$$\left(\eta^{\mu\nu}(\partial ^2)-(1-\frac{1}{\xi})\partial^{\mu}\partial^{\nu}\right)\langle 0|\mathcal{T}A_{\nu}(x)...|0\rangle = e\,\langle 0|\mathcal{T}j^{\mu}(x)...|0\rangle +…
LYg
- 1,201
10
votes
2 answers
Why does normal ordering violate the Ward identity?
It is well known that normal ordering the Lagrangian eliminates all Feynman diagrams with tadpoles$^{[1]}$. In the case of the photon self-energy in scalar QED, one of the diagrams is, in fact, a tadpole:
If one calculates $\Pi^{\mu\nu}$ neglecting…
AccidentalFourierTransform
- 56,647
9
votes
1 answer
Anomaly, symmetries, and Ward identity
I'm trying to bring together and understand the concepts of anomaly, quantum symmetries, and Ward (or Ward-Takahashi, or Slavnov-Taylor) identity in QFT. I think I know what the ideas mean, but I'm not sure if my unified understanding of the subject…
Mauro Giliberti
- 6,097
9
votes
1 answer
Some questions about Ward-Takahashi Identity
I'm a learner of Peskin and Schroeder's textbook of quantum field theory.
I have proceeded to Ward-Takahashi identity and have one question when I look for Wikipedia for reference.
The following is the Ward-Takahashi identity, where $M^{\mu}$ is…
Brioschi
- 1,055
9
votes
1 answer
Is Ward identity really satisfied by the photon's self-energy?
The one-loop self-energy of the photon,
,
when contracted with the external momentum $k^\mu$ gives the following difference of integrals where the integration variable in the first term is shifted compared to the second term.
$$ k_\mu\Pi^{\mu\nu}(k)…
Nanashi No Gombe
- 2,666
8
votes
1 answer
The Ward-Takahashi identity in Peskin and Schroeder (page 311)
I'm working on the Ward-Takahashi identity in Peskin (page 311), but I canʻt obtain Eq.(9.105) from Eq.(9.103)
According to Eq.(9.103)
\begin{align}
&i \partial_{\mu}\left\langle 0\left|T j^{\mu}(x) \psi\left(x_{1}\right)…
sky
- 199
8
votes
1 answer
Different Schwinger-Dyson Equations
In the literature on QFT there are a lot of different equations that are all called "Schwinger-Dyson equation" so I wanted to know how are they related and if they have proper names.
The first equation can be obtained by making a change of…
P. C. Spaniel
- 4,476
8
votes
1 answer
Ward Identity makes QED logarithmic divergent?
Quick question regarding superficial degrees of freedom and Ward identities.
For instance in Peskin and Schroeder it is stated that the photon-self energy is superficially quadratically UV divergent but due to the Ward identity it is only…
A friendly helper
- 81
- 1
8
votes
1 answer
Can you gauge a $U(1)_L$ symmetry?
I was recently calculating the one loop correction for the propagator of a gauge boson,
$\hspace{5cm}$
I assumed arbitrary left and right couplings, $ g _L $ and $ g _R $. I found that the one loop correction was,
\begin{equation}
= \frac{ - 4i…
JeffDror
- 9,093