All Questions
Tagged with quantum-field-theory homework-and-exercises
672
questions
4
votes
1
answer
283
views
Showing that the Ricci scalar equals a product of commutators
I have to compute the square of the Dirac operator, $D=\gamma^a e^\mu_a D_\mu$ , in curved space time ($D_\mu\Psi=\partial_\mu \Psi + A_\mu ^{ab}\Sigma_{ab}$ is the covariant derivative of the spinor ...
- 353
4
votes
1
answer
733
views
Inner product of particle-anti-particle spinor components
Suppose I have four-component spinors $\Psi$ and $\bar \Psi$ satisfying the Dirac equation with
$$\Psi(\vec x) = \int \frac{\textrm{d}^3 p}{(2\pi)^3} \frac{1}{\sqrt{2 E_{\vec p}}} \sum_{s = \pm \frac{...
- 2,319
1
vote
0
answers
743
views
How to show the oblique parameters S, T, and U are coefficients of d=6 operators
In Morii, Lim, Mukherjee, The Physics of the Standard Model and Beyond. 2004, ch. 8, they claim that the Peskin–Takeuchi oblique parameters S, T and U are in fact Wilson coefficients of certain ...
- 6,381
65
votes
2
answers
19k
views
How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$?
This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell
Show, by explicit calculation, that $(1/2,1/2)$ is the Lorentz Vector.
I see that the generators of ...
- 1,505
7
votes
1
answer
3k
views
Angular momentum operator in terms of ladder operators
I wanted to show that the angular momentum of the particle state with zero momentum $| \vec{0} \rangle$ is $0$, that is to say the intrinsic spin of a scalar field is $0$ using a mode expansion.
...
- 1,424
6
votes
1
answer
2k
views
QED BRST Symmetry
This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim:
"Consider QED ...
- 8,540
8
votes
2
answers
1k
views
Simple QFT exercise
Consider a particle on the real line with:
$L=\frac{1}{2}(\partial_0q)^2 + f(q)\partial_0q$
the equation of motion is that of a free particle $\partial_0^2q=0$. In fact $\delta[f(q)\partial_0q]=0$. ...
- 353
11
votes
3
answers
3k
views
Gauge invariant Chern-Simons Lagrangian
I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$):
$$\mathcal L= -\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + \frac{k}{4\pi}\epsilon^{\mu\nu\...
- 2,926
2
votes
0
answers
1k
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Find equations of motion from given Lagrangian density [closed]
Could someone help me solve this probably not very hard problem?
Given Lagrangian Density:
$\mathcal L=\bar{\psi}(i\gamma^\mu\partial_\mu-g\gamma^5\phi)\psi+\frac{1}{2}(\partial_\mu\phi)(\partial^\...
- 143
3
votes
2
answers
365
views
An integral related to QFT [closed]
How to show $$\displaystyle\int\int\int f(p,p')e^{ip\cdot x-ip'\cdot x}d^3pd^3p'd^3x=(2\pi)^3\int f(p,p)d^3p$$ ?
I have $p\cdot x=Et-\bf p\cdot x$
- 515
4
votes
2
answers
2k
views
The Energy-Momentum Tensor and the Ward Identity
I have a question regarding a homework problem for my quantum field theory assignment.
For the purposes of the question, we can just assume the Lagrangian is that of a real scalar field:
$$\mathcal{L}...
- 8,540
0
votes
1
answer
551
views
Representations of gamma matrices
I have to do this exercise for homework. Find a representation of the gamma matrices unitarily connected to the standard representation for wich the spinors $u(p)$ that satisfy the equation $(p_\mu \...
- 1,987