Recent content by Yaelcita

This has been most helpful. Thanks to both of you!

Let me see if I understand this correctly. What you are saying is that the only thing I know is its spinor index structure. In this case (the (1/2,1/2) case) I know my 'object' A must have one dotted and one undotted index, one from each SU(2). So I need to multiply it by another object, in...

What are van der Waerden symbols? This is the first time I've heard that expression, and there's no Wikipedia article about it... Nor can I find it in Srednicki, Peskin and Schroeder or Weinberg...

I think my question about the way things transform was unclear. This is what I mean, with an example. I know (1/2,1/2) is a Lorentz vector, so it's supposed to transform like, if A is my vector, U(\Lambda)A\, U^\dagger (\Lambda)=\Lambda A What I don't understand is how I can show that it...

If you've taken an undergraduate level QM class, it probably didn't go into as much detail as a graduate level class, so you might want to consider that. But in general, you're all ready to jump into the QFT pool. It will seem like there's stuff you're missing, but that's just because QFT is...

This is something I feel I should know by now, but I've always been very confused about. Specifically, how does one determine what each representation of the Lorentz group corresponds to? I mean, I know that the (1/2,0) and the (0,1/2) representations correspond to right and left handed spinors...

I just didn't write it, since I was working only with those two terms... I know, but I have the solution to this one problem where they then go on to define raising and lowering operators as x\pm i p_x and the same for y, and they get the Hamiltonian to look like the product of a raising and a...

Ok, let's see... Let y=y'+\frac{\varepsilon m c^2}{q B^2}. Now the Hamiltonian reads (ignoring the unimportant parts): H&=&\frac{1}{2m}\left(p_x+\frac{qB}{c}\left(y'+\frac{\varepsilon mc^2}{qB^2}\right)\right)^2-q\varepsilon\left(y'+\frac{\varepsilon mc^2}{qB^2}\right) &=&...

Homework Statement Consider a free electron in a constant magnetic field \vec{B}=B\hat{z} and a perpendicular electric field \vec{E}=\varepsilon\hat{y}. Find the energy eigenvalues and eigenfunctions in terms of harmonic oscillator eigenfunctions Hint: Use Landau gauge \vec{A}=-By\hat{x}...

Ok, there's somethign I'm missing here. You say construct little step functions that are 1/2 where sin x is greater than 1/2 and zero where it's not, right? Or in a delta neighborhood around the point where it's 1, which is the same. So the area under the step functions is infinity because each...

Ok, I'll try that for L1, but now my problem is that Mathematica doesn't agree with me! If I do the sin^2 integral in Mathematica, it says the answer is 1, but if sin^2 is less than 1, then the integral is less than the integral of 1/x^2, which is zero between - and + infinity. So my whole...

By the first one you mean the L1 one or the L2? And what do you mean by infinite step function? f=1 for all x in R? I'm not sure how this would work, because that integral would be infinite, but |sin x/x| is less than 1, so I can't conclude its integral is infinite too. And if you mean to...

Homework Statement Prove that f(x)=\sin(\pi x)/(\pi x) is in L^2(R) but not in L^1(R) This is in a chapter of the book dealing with Inverse Fourier Transform f is in L^1 if \int|f|<\infty f is in L^2 if \sqrt{\int|f|^2}<\infty Homework Equations I just have no idea how to do it The Attempt...