All Questions
8
questions with no upvoted or accepted answers
3
votes
1
answer
155
views
Non-linearities in Lagrangian of a scalar field coupled to point-like source
I have an exercise where I did not manage to understand the questions. Basically, I have this Lagrangian
\begin{equation}
\mathcal{L}=\frac{1}{2}(\partial \pi)^2-\frac{1}{\Lambda^3}(\partial \pi)^2\...
2
votes
0
answers
406
views
Derivation of Coulomb's law from classical field theory
In the section on Coulomb's law in QFT by Schwartz, he expands $-\frac{1}{4}F_{\mu\nu}^{2}$ to get $-\frac{1}{2}(\partial_{\mu}A_{\nu})^{2} + \frac{1}{2}(\partial_{\mu}A_{\mu})^{2}$, can someone ...
- 43
1
vote
0
answers
44
views
MCS Lagrangian and Euler-Lagrange
I'm trying to solve the Euler-Lagrange equation for the MCS Lagrangian density as given by Kharzeev in this article (Eqn. 7):
$$ \mathcal{L}_{\textrm{MCS}} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^{\...
- 71
1
vote
0
answers
222
views
Index notation with four-gradient
Reading Schwarz's textbook on quantum field theory, early on he gives the Lagrangian
$$\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-A_{\mu}J_{\mu}.$$
With $F^{\mu\nu}=(\partial_{\mu}A^{\nu}-\partial_{\...
user77629
0
votes
0
answers
88
views
How compute the expression of electromagnetic tensor explicitly as given here?
I am trying to understand how the second line arrives at the last line of this expression.
For $F_{\mu\nu} = \partial_\mu A_\nu -\partial_\nu A_\mu$
And $F^{\mu\nu} = \partial^\mu A^\nu -\partial^\nu ...
- 13
0
votes
1
answer
197
views
Finding the resonant frequency of a rectangular resonator filled with a magnetic material
The prompt is to find the resonant frequency $f_r$ of a rectangular resonator which is filled with a magnetic material rather than standard air or vacuum. I'm confused as how the resonance frequency ...
-1
votes
2
answers
235
views
Relativistic EM Lagrangian and the derivation of equations of motion
As mentioned in my other post, I am attempting to learn from Gross'"Relativistic quantum mechanics and field theory", and I have a question concerning the manipulation of the antisymmetric 4x4 tensors ...
- 255
-3
votes
1
answer
204
views
What does “Integrating out field” mean?
In Schwartz’s QFT book, there is a couple of exercise problems of particle polarization in chapter 3. I have trouble with finding interaction terms from the given Lagrangians. Is it just okay to ...
- 1