All Questions
12
questions
2
votes
2
answers
151
views
Derivation of propagator for Proca action in QFT book by A.Zee
Without considering gauge invariance, A.Zee derives Green function of electromagnetic field in his famous book, Quantum Field Theory in Nutshell. In chapter I.5, the Proca action would be,
$$S(A) = \...
- 629
2
votes
1
answer
131
views
Fermion number non-conservation in parallel $E$ and $B$ fields
This is from Problem 19.1 in Peskin and Schroeder.
(a) Show that the Adler-Bell-Jackiw anomaly equation leads to the following law for global fermion number conservation: If $N_R$ and $N_L$ are, ...
- 409
-3
votes
1
answer
204
views
What does “Integrating out field” mean?
In Schwartz’s QFT book, there is a couple of exercise problems of particle polarization in chapter 3. I have trouble with finding interaction terms from the given Lagrangians. Is it just okay to ...
- 1
0
votes
2
answers
176
views
Building Lagrangians for Classical Field Theory
I've been studying quantum mechanics and classical field theory for quite a while now. However, I still struggle with the idea of building scalars from vectors and tensors for the Lagrangian density.
...
- 1
0
votes
1
answer
105
views
Simple question on quantization of EM field
This is part of the lecture note of QFT by Tong:
I have a question on the last part of (6.27). Why does it hold? Actually this question is not about QFT and is about just integral. The typical way to ...
- 1,081
3
votes
1
answer
155
views
Non-linearities in Lagrangian of a scalar field coupled to point-like source
I have an exercise where I did not manage to understand the questions. Basically, I have this Lagrangian
\begin{equation}
\mathcal{L}=\frac{1}{2}(\partial \pi)^2-\frac{1}{\Lambda^3}(\partial \pi)^2\...
-1
votes
1
answer
74
views
Determination of energy density state for an electromagnetic field
I've got this problem to solve:
Consider the next electromagnetic field:
$|A\rangle=\frac{1}{\sqrt{N!}}\left ( \int e^{-k^2} \boldsymbol{a}^\dagger_{k,+} \right )^N |0\rangle$. Find the mean ...
- 3
1
vote
1
answer
135
views
Maxwell theory duality problem
I have to show that
$$q \equiv \int d^{3}\vec{x}\, J^0 = -\int d^{3}\vec{x}\ \partial_i F^{0i} = -\int \frac{1}{2} d^{3}\vec{x}\ \varepsilon^{ijk} \partial_{i}G_{jk} \tag{1}$$
(this is exactly what ...
- 2,188
11
votes
3
answers
2k
views
Propagator of Maxwell-Chern-Simons theory
I need to compute the "topologically massive photon" propagator.
I've started with:
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{\mu}{4}\epsilon^{\mu\nu\lambda}A_\mu\partial_\nu ...
- 929
1
vote
1
answer
515
views
1
vote
0
answers
182
views
$E$ and $B$ fields in Axial Gauge
I am trying to compute the $\vec{E}$ and $\vec{B}$ fields in the Axial gauge ($n \cdot \vec{A}=0$) where $n^2=1$, but I'm having trouble seeing the usefulness/how it simplifies the equations.
- 11
2
votes
1
answer
111
views
A question about verifying the transverse of electric field
I came accross a question about verifying the transverse of electric field in Peskin and Schroeder's QFT p179.
Given
$$ \mathcal{A}^{\mu}(\mathbf{k}) = \frac{ -e}{| \mathbf{k} | } \left( \frac{p'^{...
- 6,401