All Questions
Tagged with quantum-field-theory homework-and-exercises
672
questions
65
votes
2
answers
19k
views
How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$?
This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell
Show, by explicit calculation, that $(1/2,1/2)$ is the Lorentz Vector.
I see that the generators of ...
- 1,505
63
votes
0
answers
4k
views
How to apply the Faddeev-Popov method to a simple integral
Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
- 1,210
24
votes
3
answers
7k
views
Problem understanding the symmetry factor in a Feynman diagram
I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are ...
- 6,067
17
votes
3
answers
7k
views
How to obtain the explicit form of Green's function of the Klein-Gordon equation?
The definition of the green's function for the Klein-Gordon equation reads:
$$
(\partial_t^2-\nabla^2+m^2)G(\vec{x},t)=-\delta(t)\delta(\vec{x})
$$
According to these resources:
Green's function ...
- 6,095
16
votes
2
answers
5k
views
How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?
I'm trying to compute the angular momentum
$$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$
where ${T^\mu}_\nu=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\partial_\nu\phi-{\delta^\mu}_\...
user24999
16
votes
1
answer
320
views
Degeneracy in mass of $8$ and $27$ reps of $SU(3)$ in Coleman's Aspects of Symmetry
In Coleman's Aspect of symmetry he proposes an amusing problem in the first chapter. It asks us to consider a set of eight pseudo-scalar fields transforming in the adjoint representation of $SU(3)$. ...
- 161
16
votes
0
answers
7k
views
Quantum Field Theory and the Standard Model by Matthew Schwartz - Solution's manual [closed]
Is there a way I can find a solution's manual for Matthew Schwartz's "Quantum Field Theory and the Standard Model" book?
15
votes
3
answers
4k
views
Three integrals in Peskin's Textbook
Peskin's QFT textbook
1.page 14
$$\int_0 ^\infty \mathrm{d}p\ p \sin px \ e^{-it\sqrt{p^2 +m^2}}$$
when $x^2\gg t^2$, how do I apply the method of stationary phase to get the book's answer.
2....
- 5,971
14
votes
2
answers
5k
views
Position operator in QFT
My Professor in QFT did a move which I cannot follow:
Given the state $$\hat\phi|0\rangle = \int \frac{d^3p}{(2\pi)^3 2 E_p} a^\dagger_p e^{- i p_\mu x^\mu}|0\rangle,$$ he wanted to show that this ...
- 263
12
votes
1
answer
5k
views
Bessel function representation of spacelike KG propagator
Preliminaries: In their QFT text, Peskin and Schroeder give the KG propagator (eq. 2.50)
$$
D(x-y)\equiv\langle0|\phi(x)\phi(y)|0\rangle = \int\frac{d^3p}{(2\pi)^3}\frac{1}{2\omega_\vec{p}}e^{-ip\...
- 695
12
votes
2
answers
6k
views
Angular Momentum Operator in Quantum Field Theory
I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...
- 519
11
votes
4
answers
3k
views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
$$\int\frac{d^4k}{(2\pi)^4}\,\frac{1}{(k^2)^2}e^{ik\cdot\epsilon}=\frac{i}{(4\pi)^2}\log\frac{1}{\epsilon^2},\...
- 1,701
11
votes
3
answers
3k
views
Gauge invariant Chern-Simons Lagrangian
I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$):
$$\mathcal L= -\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + \frac{k}{4\pi}\epsilon^{\mu\nu\...
- 2,926
11
votes
3
answers
2k
views
Propagator of Maxwell-Chern-Simons theory
I need to compute the "topologically massive photon" propagator.
I've started with:
$$
\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{\mu}{4}\epsilon^{\mu\nu\lambda}A_\mu\partial_\nu ...
- 929
11
votes
1
answer
622
views
The problem in Sredniki's textbook: How do I calculate loop corrections for $\phi\phi\to\phi\phi$ with this Lagrangian?
The problem in Sredniki's textbook 10.5 :
For a free scalar field $\psi$, the Lagrangian is
$$\cal{L}= -\frac{1}{2}\partial^\mu\psi\partial_\mu\psi-\frac{1}{2}m^2\psi^2$$
Here we use the metric $\...
- 5,971