Recent content by Xico Sim

A set B of vectors (in this case matrices) is a basis of a vector space V if and only if any element of V can be written as a linear combination of the elements of B (i.e. B spans V) and the elements of B are linearly independent. In order to show that B spans V=##\mathfrak so(4)##, you can...

Sorry, but I still have the same problem I had before: Hm I think your second equal sign is unjustified. Let me try and compute that: ##U^{-1}=e^{-itX}=e^{-itX^{\dagger}}=e^{(itX)^{\dagger}}=(e^{itX})^{\dagger}=U^\dagger## As expected. (I used the assumption that ##X## is hermitian on my...

I don't see how... maybe I'm missing something trivial?: Suppose ##U^{-1} = X##. Then, $$U^{-1}U \approx -X(I + i \epsilon X) = -X - i \epsilon X^2 \ne I$$ Which is absurd. Two questions about this part: You wrote ## X=exp(U) ##. But ##X \in \mathbf{g}## and ##U \in \mathbf{G}##, so I would...

I understand that. What I want to know is why they do it. Also, why the characteristics one finds for ##X## in such an approximated formula for ##U## (e.g. one finds that ##X## is hermitian in the su(2) case) transfers to all elements of g. Finally, I think I've seen people refer to such an...

Hi! I'm studying Lie Algebras and Lie Groups. I'm using Brian Hall's book, which focuses on matrix lie groups for a start, and I'm loving it. However, I'm really having a hard time connecting what he does with what physicists do (which I never really understood)... Here goes one of my questions...

What is PR?

When determining ##X##?

To make myself clear, I posted my attempt. I arrived at the correct wavefunction, but I have a problem with it: even though it seems symmetric, I would expect it to be only mixed symmetric (only symmetric in 1,2), since ##X## is only symmetric in 1,2 and ##\phi## is completely symmetric...

What if it's the weak interaction? Should't the matrix elements behave the same way?

Using Thomson's book I understood the derivation of the proton spin-flavour wavefunction. I will try to apply what I learned to this case.

The problem is that I did not understand the derivation of the proton wavefunction also: I found Griffiths, and for that matter every other text I found on the subject, quite confusing. Do you happen to know a place where it is clearly and thoroughly explained?

Hi, guys. If I want to write the spin-flavor wavefunction of ##\Sigma_+## starting only from knowing that the quark content of the proton is ##uud##, how can I procced? I started by applying the ladder operators in order to get the baryon octet vertexes. I am now having problems with...

Well, as I understand it now, people use ##uud## as written above as an abbreviation...

"So"? i don't see why...

Hi, guys. In Povh's book, page 198, he says: "The strong force conserves the strangeness S and so the neutral kaons are in an eigenstate of the strong interaction." I do not see why this must be the case. My atempt to understand it: $$ŜĤ_s |K_0 \rangle = Ĥ_sŜ |K_0 \rangle$$ So $$Ŝ(Ĥ_s |K_0...