Recent content by rntsai

Just a suggestion, but a lot of this already exists in other computer algebra software... MAGMA and GAP have these. GAP is my favorite (and it's free). You might want to look into what they have and add any extra constructions on top. For example, the mathematica notebooks you posted earlier...

I'm trying to calculate the pauli-lubanski pseudo vector for different representations of the poincare group. The first rep is the infinite dimensional "angular momentum" rep where the generators of the lorentz part take the form : M_ab = x_a*d_b - x_b*d_a (for 3 rotations) M_ab =...

To be honest (and going out on a limb a little), I'm not sure a definition is necessary! (I'm fairly conservative by nature so I won't go much beyond this). The bit on the isomorphic groups doesn't seem right. Reducability can change if the base field is changed (complexes vs. reals for...

Actually I didn't catch that before...at any rate I'm actually doing my claculations at the algebra level (so these are all reps of A1+A1 or D2 over the reals or over the complexes). this let's me defer complications related to signature, covering groups,...until later. I think you meant...

Thanks for the clear answer...as a followup question (and I have several more of these;-) does labeling reps of SL(2,C)xSL(2,C) with a single "spin" make sense? what's the "spin" of an (n,m) rep? what about (n1,m1)+(n2,m2)?...

I don't think I have much insight into the geometry of these reps, so I can't address what you're asking...I am testing my understanding of the 4 dim reps of the group by trying different combinations : (1/2,0) + (1/2,0) (not faithful) (1/2,0) x (1/2,0) = (1,0) + (0,0) (not...

I posted too quickly (couldn't figure out how to delete the post). It does look like they are different...sorry about that

I'm reading the wiki article on Representation theory of the Lorentz group and they seem to make a distinction between these two reps: (1/2,1/2) and (1/2,0) + (0,1/2) I did some checks and it seems that these two are the same. Am I wrong or is the wiki article wrong (won't be the...

Actually both of you are way off...we probably do speak different languages and a lot is being lost in the translation... let's leave it at that.

what! what calculations can you do in "physics" that you can't do mathematically. you are really mixing all sorts of objects here. Let's restrict to the "scalar" case (R^4 to C). We can deal wil spin 1/2, spin 1,... independantly. For example for spin 1/2 : how do you distinguish between...

OK, so how do you distinguish between waves? so if I give you a wave function (as in a map from R^4 to C) how can you tell if this corresponds to a photon, or a neutrino...or the entire universe for that matter.

It's not very clear what you mean by "metric for the vector space on which ... " but I think the quick answer is no...they have nothing to do with each other. For one the killing form (metric) is over an N_g dimensional space where N_g is the number of infinitesimal generators of the group...

I think I do. Here's a list of the eigenvalues (any linear combination of these would also do) for the 8 rep (gluons) g^3,g^8 1 ,0 -1 ,0 1/2 ,sqrt(3)/2 -1/2 ,-sqrt(3)/2 1/2 ,-sqrt(3)/2 -1/2 ,sqrt(3)/2 0 ,0 0 ,0 for the 3 rep (quarks) 1/2...

Things are beginning to clear up. What I was calling "isospin" looks like what you call "colour isospin". SU(3)_color is the SU(3) in the standard model and the weights of it's reps will give you "color isospin" and "color hypercharge". Gluons do not have zero "color isospin"; (actually 2 do...

It shouldn't matter what space we're in, an SU(3) octet is an SU(3) octet. It's weights (eigenvalues of certain elements) will follow a well defined combination. These elements might well have completely different definitions, but that doesn't change the eigenvalues. Are you saying that...