All Questions
Tagged with gauge-theory ward-identity
23
questions
3
votes
0
answers
74
views
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
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
- 51
0
votes
0
answers
48
views
Ward identity in scalar QED; gauge transformations & plane wave solutions for polarization
I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian:
$$
L = -\frac{1}{4}...
2
votes
0
answers
83
views
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 ...
- 310
4
votes
0
answers
107
views
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 ...
- 1,421
4
votes
1
answer
349
views
On the Ward Identity in QED
I am reading P&S, particularly Chapter 5.5. The authors are trying to derive an expression for the Ward identity (not formally, but still). They claim that the amplitude describing a photon ...
- 3,992
4
votes
0
answers
221
views
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 $$S[X,g]...
- 2,923
6
votes
2
answers
896
views
Ward Identity and Proca Fields
I'm following the book Quantum Field Theory and the Standard Model by Schwartz and I came to the rigorous non-perturbative proof of the Ward identity with path integrals via the Schwinger-Dyson ...
- 127
9
votes
1
answer
2k
views
Anomaly, symmetries, and Ward identity
I'm trying to bring together and understand the concepts of anomaly, quantum symmetries, and Ward (or Ward-Takahashi, or Slavnov-Taylor) identity in QFT. I think I know what the ideas mean, but I'm ...
- 5,931
2
votes
0
answers
128
views
Is unitarity equivalent to imposing Ward identity in $U(1)$ gauge theory?
I proved in a gauge theory lecture that unitarity violation implies ward identity violation in the simple $U(1)$ case.
I was wondering if this statement can be reversed, i.e can we say that unitarity ...
1
vote
1
answer
221
views
Why does this amplitude not vanish by the Ward identity?
Consider the process $e^-\rightarrow e^-\gamma$ depicted in the following Feynman diagram.
The spin-averaged amplitude with linearly polarised photons is
$$\overline{|M|^2}=8\pi\alpha\left(-g^{\mu\nu}...
- 1,187
3
votes
1
answer
521
views
Ward identity prohibits mass of photon
On wikipedia one can read the following statement:
The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of ...
- 213
1
vote
0
answers
92
views
QCD gauge invariant amplitude?
In order to keep the correct degrees of freedom (which are 2) for massless gauge fields one imposes,
$$p^\mu \epsilon_\mu = 0 \tag1$$
Together with the gauge redundacy/equivalence relation,
$$\...
- 1,597
0
votes
0
answers
93
views
Is there a relation between various vertices in Yang-Mills theory?
In Yang-Mills theories (and more complicated theories with additional matter fields) we have three and four gauge boson vertices, boson-ghost and boson-matter vertices. Perturbative divergences ...
- 2,191
5
votes
0
answers
569
views
Ward Identity in non-abelian gauge theories
While in QED correlation functions including the photon field vanish when the Lorentz index of the gauge field is contracted with its own momentum (this fact is usually referred to as Ward Identity, ...
- 51
10
votes
2
answers
1k
views
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 ...
