Yeah, I realized that last night when I was showering.
However, I can't seem to find a curve that will actually suit all of the conditions, namely that:
f(t) = a(t)g + b(t)g' with b(t) + a(t) = 1 from the bottom right corner and that a(t)cos(x) + b(t)cos(y) = cos(z) and a(t)sin(x) + b(t)sin(y)...
Would it then work to say that you can take the function f: [0,1] -> G, where f = tg + (1-t)g' with g, g' members of G. f(0) =g and f(1) = g' so G is indeed connected?
Or am I missing something here?
Homework Statement
Show that the group G where G = \left(\begin{array}{ccc} \cos\theta & -
sin\theta & u \\ \sin\theta & \cos\theta & v \\ 0 & 0 & 1 \end{array} \right) u,v \in \Re, \theta \in \Re/2\pi Z
Homework Equations
I know that a set is connected if it is not the disjoint...
So, the upper light cone has a Lorentz invariant volume measure
dk =\frac{dk_{1}\wedge dk_{2} \wedge dk_{3}}{k_{0}}
according to several sources which I have been reading. However, I've never seen this derived, and I was wondering if anyone knew how it was done, or could point me towards...
Ah, that makes quite a lot of sense.
What if, on the other hand, you have a term like i \epsilon_{\alpha \mu \beta \nu} k'_{\alpha}k_{\beta}P^{\mu} P^{\nu}? k, k' and P are all 4-vectors. How would you be able to evaluate this?
Hi all.
I'm working on a project at the moment, and I've run into some questions regarding the 4-d Levi Civita tensor contracted with the metric tensor.
I'm working on finding the cross-section for neutrino-proton scattering. While ccontracting the hadronic and leptonic tensors, I end up...
To be honest, almost every deadline for REUs has passed by this point. You'll have to carefully look at every site to see if there are any that are still open and give funding to internationals. You'll have better luck next year if you look in advance.
I guess I should also say I'm not sure if the magnetic field from the solenoid is correct; for the force to have a maximum at any point along the solenoid, would the magnetic field not have to be changing?
Homework Statement
A long circular solenoid of radius a and N turns per unit length has its axis in the z direction. A small highly conducting ring, or area A, resistance zero but self inductance L, is place with its plane horizontal and its centre on the axis and near the top of the...
Have been more or less rejected from UWash, but got an offer from Colombia today to work on ATLAS. A bit regretful I already had to accept the position at Fermilab.
I believe that recommendations are very important. Both of the programs I've been accepted into (for physics) have mentioned that I had very strong recommendations, in addition to a 4.0 GPA.
So, if you don't get in anywhere this year, I'd recommend spending next year forming a close...