Tagged Questions
4
votes
2answers
60 views
How to directly calculate the infinitesimal generator of SU(2)
We commonly investigate the properties of SU(2) on the basis of SO(3). However, I want to directly calculte the infinitesimal generator of SU(2) according to the definition $$X_{i}=\frac{\partial ...
0
votes
0answers
45 views
Gradient involved commutator in $\phi^4$ theory
In a phi fourth theory, the Hamiltonian density is:
$$\mathcal{H}=\frac{1}{2}\pi^2+\frac{1}{2}(\nabla \phi)^2+\frac{1}{2}m^2\phi^2+\frac{\lambda}{4!}\phi^4$$
Now I impose the usual equal time ...
0
votes
1answer
75 views
Derivation of Dirac equation using the Lagrangian density for Dirac field
How can I find Dirac equation using the Lagrangian density for Dirac field?
0
votes
0answers
37 views
Question regarding operators and cylindrical coordinates
I have the following problem in my hand:
I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$
to this expression:
...
2
votes
0answers
28 views
5D Ricci Curvature
As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper ( http://arxiv.org/pdf/1107.5563v2.pdf ). I was wondering if there is some ...
4
votes
0answers
58 views
I am trying to calculate the branching ration of higgs goes to 2 photons using the standard model [closed]
I need to use the three lowest order feynman diagrams to first calculate the squared matrix element to put into fermis golden rule formula and then from there get the branching ratio of higgs decays ...
-2
votes
0answers
52 views
Mass of classical kink [closed]
related post Solving the soliton equation without energy
The energy density of kink solution is
$$\epsilon(x)= \frac{1}{2}(\frac{d \phi}{dx})^2+ V(\phi)$$
where the potential
$$V(\phi)= ...
9
votes
4answers
357 views
Trace and adjoint representation of $SU(N)$
In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as
$$ (t^a_G)_{bc}=-if^{abc} $$
The following identity can be found in Taizo Muta's book "Foundations of Quantum ...
0
votes
1answer
84 views
4
votes
2answers
147 views
A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
0
votes
0answers
66 views
How would I apply Wick's theorem to expand the time-ordered product of three quantum fields? [closed]
I think I understand how to use Wick's theorem to expand the time-ordered product of quantum fields, but I'd like to confirm that. Could you apply Wick's theorem to:
...
1
vote
2answers
114 views
Regarding real field Klein Gordon Equations
Here are 2 doubts:
If we change the sign of the mass term in the free massive KG Lagrangian to get:
$L = \frac{1}{2}\partial^\mu\phi\partial_\mu\phi + \frac{1}{2}m^2\phi^2$,
What would be the ...
1
vote
0answers
78 views
Massless Dirac equation is Weyl covariant
Does somebody know how to show that the following equation is Weyl invariant?
$$\gamma^ae_a^\mu D_\mu \Psi=0$$
where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
1
vote
1answer
201 views
Dirac Equation in General Relativity
Dirac equation for the massless fermions in curved spase time is $γ^ae^μ_aD_μΨ=0$, where $e^μ_a$ are the tetrads. I have to show that Dirac spinors obey the following equation:
...
1
vote
0answers
72 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 ...
3
votes
1answer
106 views
Inner product of particle-anti-particle spinor components
Suppose I have four-component spinors $\Psi$ and $\bar \Psi$ satisfying the Dirac equation with
$$\Psi(\vec x) = \int \frac{\textrm{d}^3 p}{(2\pi)^3} \frac{1}{\sqrt{2 E_{\vec p}}} \sum_{s = \pm ...
1
vote
0answers
104 views
How to show the oblique parameters S, T, and U are coefficients of d=6 operators
In Morii, Lim, Mukherjee, The Physics of the Standard Model and Beyond. 2004, ch. 8, they claim that the Peskin–Takeuchi oblique parameters S, T and U are in fact Wilson coefficients of certain ...
3
votes
1answer
717 views
How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?
This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.)
Show, by explicit calculation, that ...
3
votes
1answer
248 views
QED BRST Symmetry
This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim:
"Consider QED ...
3
votes
2answers
198 views
Simple QFT exercise
Consider a particle on the real line with:
$L=\frac{1}{2}(\partial_0q)^2 + f(q)\partial_0q$
the equation of motion is that of a free particle $\partial_0^2q=0$. In fact $\delta[f(q)\partial_0q]=0$. ...
5
votes
2answers
275 views
Gauge invariant Chern-Simons Lagrangian
I have to prove the (non abelian) gauge invariance of the following lagrangian (for a certain value of $\lambda$):
$$-\frac14 F^{\mu\nu}_aF_{\mu\nu}^a + ...
1
vote
0answers
315 views
Find equations of motion from given Lagrangian density [closed]
Could someone help me solve this probably not very hard problem?
Given Lagrangian Density:
$\mathcal ...
3
votes
2answers
554 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:
...
1
vote
1answer
262 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 ...
