This is probably a dumb question, but I have a book that claims that if you have a function of the momentum squared, f(p2), that:
\frac{d}{dp^2}f=\frac{1}{2d}\frac{\partial }{\partial p_\mu}
\frac{\partial }{\partial p^\mu}f
where the d in the denominator is the number of spacetime...
I want to show that the binomial distribution:
P(m)=\frac{n!}{(n-m)!m!}p^m(1-p)^{n-m}
using Stirling's formula:
n!=n^n e^{-n} \sqrt{2\pi n}
reduces to the normal distribution:
P(m)=\frac{1}{\sqrt{2 \pi n}} \frac{1}{\sqrt{p(1-p)}}
exp[-\frac{1}{2}\frac{(m-np)^2}{np(1-p)}]...
Does anyone know what is meant by electrical isolation?
From this schematic:
url=http://upload.wikimedia.org/wikipedia/en/1/12/Swer.gif
I don't see the significance of calling the transformer an "isolation transformer". What is the difference between a transformer and an isolation...
How can the derivative of a basis vector at a point be the linear combination of tangent vectors at that point?
For example, if you take a sphere, then the derivative of the polar basis vector with respect to the polar coordinate is in the radial direction. How can something in the radial...
If you walk at constant latitude with your arm always sticking towards the North pole, is that parallel transport of your arm?
The equations don't seem to say it is.
The vector field would be \vec{V}=V(\theta)e_\theta . The component of the vector only depends on theta, but at constant...
I can no longer click on a Latex image in a post and grab the code for it. Is there a way to do this? It used to be click on the image, the code would come up, and then copy and paste. Now I don't know what to do.
Say you touch the hot wire and a piece of plumbing simultaneously. Then current flows through the hot wire, through you, to the ground, and I assume (though I'm not sure) to where the ground wire is tied to the neutral wire (at the breaker panel). But is the current in the ground mainly through...
Why do 400 kv power lines have 6 pairs of wires, 3 on each side? Shouldn't there only need to be 4 wires, a ground/neutral wire and 3 wires for 3 phases?
If you have a two-wire transmission line that is open-ended at the load, and connected to an alternating voltage generator at the source, then the voltage between the open ends can be as high as twice the voltage of the generator. However, if the two ends are shorted, then the voltage would be...
Can you make a microwave oven by taking a microwave generator and attaching one lead to one side of a metal box, and the other lead to the other side of the metal box, and putting food in the box and flipping the switch on? If this is possible, can you take a can of food and put two leads across...
How does lightning cause a voltage spike? Is it the changing magnetic field caused by the lightning current that induces an emf in the power lines, or are electric charges deposited on the actual lines (like a battery pushing charges). Is it possible for the emf of the lightning to cancel the...
If a hot power line hits the ground, and you are touching the neutral line with your hands and the ground with your feet, would you get shocked?
Also, same question, except the lines are coming out of a grounded portable generator instead of the electric company.
Say you have a square room with only one door, and the door is as the center of one side of the square. Suppose you put a stereo just outside the door. Can you hear the sound if you are standing in one of the corners of the room that's adjacent to the door?
Fraunhofer diffraction predicts that...
According to Wikipedia the formula for the field created by an aperture (the Kirchoff-Fresnel Integral) is:
\Psi(r)\propto \int\!\!\!\int_\mathrm{aperture} E_{inc}(x',y')~ \frac{e^{ik | \bold r - \bold r'|}}{4 \pi | \bold r - \bold r' |} \,dx'\, dy'...
Can renormalization of QED really be interpreted as a dielectric shielding of the vacuum by electron/positron pairs that appear and disappear out of the vacuum?
I understand that's what the Feynman diagram for the QED vertex suggests, since it's the internal fermion lines that interact with a...
I still don't understand antisymmetry and fermions.
Is the proton wavefunction equal to this:
|\psi_p>=\frac{1}{\sqrt{6}}\left(2|u\uparrow u\uparrow d \downarrow \rangle -
|u\uparrow u\downarrow d \uparrow \rangle -
|u\downarrow u\uparrow d \uparrow \rangle \right)
or this...
Should one view correlation functions as:
(1) \; \langle T{\phi(x)\phi(y)}\rangle
or
(2) \; \langle T{\phi(x)\phi(y)}\rangle - \langle \phi(x)\rangle \langle\phi(y)}\rangle
with the second term being zero?
(2) makes more sense as it really measures whether the two fields are...
definition of "indistinct" in pauli exclusion principle
I'm a little confused about what constitutes a distinct particle.
For example, a muon is not an electron as they've got different masses. So the wavefunction for the electron/muon system does not have to be antisymmetric (although it can...
Why is a deuteron an antisymmetric singlet in isospin:
|\uparrow\downarrow>-|\downarrow\uparrow>=|0,0>
whereas a proton and neutron that are separated are a combination of an antisymmetric singlet and a symmetric triplet:
|\uparrow\downarrow>=|0,0>+|1,0>
I don't understand the difference...
Why is it that the group SU(6) gives you the correct wave function for hadrons made up of the u, d, and s quarks? The 6 elements in the fundamental representation would be u up, u down; d up, d down; s up, s down. What's the meaning behind SU(6)?
Also, for 6 quarks, would it be SU(12)?
Not every state can be represented by a direct product. Do states that can be written as a direct product have anything special about them?
It seems that states that can be written as a direct product lose correlation between between each individual state. More specifically, stronger than...
I have some basic questions on bonds.
Take two identical particles in their ground state. When separated, the Hamiltonian can be written as the matrix:
1 0
0 1
where 1 is the energy.
When brought close together, there is the possibility of transitions through off-diagonal terms, and the...
I've got a question about Fourier transforms.
Say you have the integral:
D(x,y)=\int \frac{d^4k}{2 \pi^4} \frac{e^{ik(x-y)}(.5+.5\frac{\vec{k}^2}{k_{0}^2})}{k^2+i\epsilon}
Can I just set this equal to:
D(x,y)=\int \frac{d^4k}{2 \pi^4} \frac{e^{ik(x-y)}}{k^2+i\epsilon}
since...
Why are spin 0 mesons pseudo-scalar, and spin 1 mesons vector?
Why can't spin 0 mesons be scalar, and spin 1 mesons be pseudo-vector?
If observables are bilinear in the fields, then how can you even detect whether a field is pseudo-scalar, since \phi^2 is a scalar no matter if the meson field...
Why if you shine a flashlight on the wall, the circle of light is bigger than the opening of the flashlight (the aperture)?
If I attach a pipe (of the same radius as the opening of the flashlight) to the aperture so that light has to go through the pipe, then geometrically the circle of light...
Why is a laser monochromatic? I read somewhere that the reason is because of a Fabry-Perot cavity, and not necessarily because of stimulated emission, so that if you have an ordinary light bulb in such a cavity, it would produce monochromatic waves.
Can you just send the stimulated light...
This is probably an easy question, but my math is not good enough to answer it.
For Gaussian integrals:
\frac{\int \Pi_i [dx_i] x_k x_l e^{-\frac{x_i A_{ij} x_j}{2}}} {\int \Pi_i [dx_i] e^{-\frac{x_i A_{ij} x_j}{2}}}=A^{-1}_{kl}
As far as I understand it, in QFT, Aij is a local operator. So...
I don't understand how to find the irreducible representations of a group.
Under transformation U: (T')^{ijk}=U^{il}U^{jm}U^{kn}T^{lmn}
But suppose (M')^{ijk}=(T')^{ijk}+\pi (T')^{jik}
Then (M')^{ijk}=U^{il}U^{jm}U^{kn}T^{lmn}
+\pi U^{jl}U^{im}U^{kn}T^{lmn}=U^{il}U^{jm}U^{kn}(T^{lmn}+\pi...
For diffraction you can assume slits in screens contain sources for the diffracted waves.
But for a slit of finite width, how far apart are the sources? If the sources are continuously placed in the gap, then that means there are an infinite number of sources. An infinite number of sources...
Just to review a little bit:
In general, for a gauge field with Yang-Mills Lagrangian
\mathcal L=-\frac{1}{4}F^{c}_{\mu \nu}F^{c \mu \nu}
for each c it is impossible to find the resulting free Green's function G(k) in momentum space:
(g^{\mu \nu}k^2-k^{\mu}k^{\nu})G_{\nu...