All Questions
16
questions
3
votes
0
answers
66
views
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 ...
- 370
0
votes
1
answer
376
views
Ward identity of correlation function
For local observables $\{O_i(x_i)\}^n_{i = 1}$, one defines the Ward identity as
$$\partial_{\mu}\langle j^{\mu}(x)\prod^n_{i = 1}O(x_i)\rangle = \sum^n_{i = 1}\delta(x-x_i)\langle O_1(x_1)\cdots\...
user361492
4
votes
1
answer
153
views
Different version of conformal Ward identity
In the book by Di Franceso, Mathieu, Senechal, equation (5.46) shows that (assuming $\bar\epsilon = 0$)
$$
(*) \qquad \langle \delta_{\epsilon, 0} \mathcal{O}\rangle
= - \oint_\infty \frac{dz}{2\pi i ...
- 41
5
votes
1
answer
372
views
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,
$$ \...
- 352
2
votes
0
answers
52
views
Do Ward identities imply that there is an (effective) Lagrangian invariant under the symmetry?
In usual perturbative QFT, if the UV Lagrangian is invariant under a symmetry $G$ and the regularization of the path integral does not break $G$, the Feynman rules are explicitly invariant under $G$. ...
- 461
4
votes
1
answer
234
views
Conformal invariance in 2d and correlation functions
It is well-known that 2d global conformal invariance constrains the 2, 3-point functions to some very simple form, and 4-point function must be
$$
f(\eta, \bar \eta) \prod_{i < j}z_{ij}^{...} \bar ...
- 325
4
votes
1
answer
249
views
Symmetry implies Ward identity
I am thinking about symmetries and that their "quantum" consequences are Ward identities of the form $$<\beta|[Q,S]|\alpha>=0,$$ where $Q$ is the conserved charge associated with the ...
- 3,992
3
votes
1
answer
482
views
Is the 1PI self-energy of a massive photon transverse? EDIT: Upsetting consequences for the photon mass and renormalizability
Suppose we had the Lagrangian:
$$\mathcal{L} = -\frac{1}{4} F^{\mu \nu}F_{\mu \nu} + \overline{\psi} (i \gamma^{\mu}\partial_{\mu} -m)\psi -e\overline{\psi} \gamma_{\mu} \psi A^{\mu} +\frac{1}{2} m_{\...
4
votes
1
answer
720
views
Is there a formulation of Noether’s theorem for the path integral formalism?
The notion that conserved quantities (or quantities for which there is something like a continuity equation) correspond to symmetries of the action of a physical system can be formulated in various ...
- 6,763
4
votes
1
answer
1k
views
Proof of Ward-Takahashi Identity in Peskin and Schroeder page 311
I am studying the derivation of Ward Takahashi identity using Peskin and Schroeder (Page number 311)
What I understand from his statements is as follows,
for a change of variables
\begin{equation}
...
- 545
2
votes
1
answer
199
views
Ward identities without time-ordering
In the book Conformal Quantum Field Theory in D-Dimensions, they state on pg. 181 the following two identities in relation to Ward identities of an Abelian internal symmetry (so the infinitesimal ...
- 992
-1
votes
1
answer
346
views
Why does the violation of Ward identity not require cancellation of global anomalies?
This question is a continuation of the answer posted for this question about anomalies.
Is there a violation of the Ward identity associated with an anomalous global symmetry? If yes, why is the ...
- 26.8k
4
votes
1
answer
585
views
Why should Ward identities only be used with the effective action (as opposed to the generating functional for connected diagrams)?
My question is about the derivation of Ward identities. I will sketch it here in the case of an O(N) symmetric model and point out what it bothering me when I am done. I am being very sloppy with the ...
- 4,385
8
votes
1
answer
325
views
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 ...
- 8,995
5
votes
1
answer
2k
views
Traceless of stress-energy tensor in $d=2$
This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function
$$
S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right>
$$
He then ...
- 26.6k