Recent content by Zorba

I would be more of a theoretician, but recently I have been somewhat interested in trying to learn about recent results (last 30 years or so) in experimental high energy physics - about the implications or results from collision experiments and so on. I realize this is asking a lot, but is...

Howard Georgi wrote a book called "Lie Algebras In Particle Physics: from Isospin To Unified Theories (Frontiers in Physics)" Are there any other books like this one - that covers the same stuff - except that uses a more mathematically formal tone? I know representation theory and some the...

Yes, because if you rearrange the Jordan blocks, then you just have to rearrange the corresponding eigenvectors in the similiarity matrix, so this definition where he requires the Jordan blocks to be placed in a certain order is a bit stupid for this exact reason. Fine, if it lends itself to...

Using the isomorphism theorems here seems like "killing a fly with a nuke" or whatever the saying is (although your idea of that homomorphism does seem interesting.) micromass seems to have covered the rest.

That sounds about right. Look at the definition in your book of a Jordon block matrix, does he say anything about the placement of Jordan blocks according to their multiplicities?

Note the use of "according to his clock" so time dilation comes into effect. According to the article the 1516c figure refers to star trek (I think?) spaceship drives, and using wikipedia (d=24,900 ± 1,000 ly to centre of milky way) and obviously neglecting all relativistic effects I get a...

Thanks for the reply, but I don't think 1 can't be iso to 8 because they have different orders. Also I toyed with including 7 with 2,9, but I didn't in the end, I think you're probably right though, for some reason I thought <{1}> has order 3, damn it...

Just had an exam there, one of the questions was Partition the list of groups below into isomorphism classes 1.\mathbb{Z}_8 2.\mathbb{Z}_8^* (elements of Z_8 relatively prime to 8) 3.\mathbb{Z}_4 \times \mathbb{Z}_2 4.\mathbb{Z}_{14} \times \mathbb{Z}_5 5.\mathbb{Z}_{10} \times...

Are you familiar with the Rank-Nullity Theorem?

No - one reason to see immediately why, is because if it was true, then Lagrange's theorem should be a two way implication. Simplest example via wikipedia is \mathbb{A}_4 with has order 12 and no subgroup of order 6.

Ah, yes I see it now, thanks for that.

Can anyone describe to me the path a low mass body takes as it leaves the main-sequence? Or is it the case that a low mass body just moves along the main sequence, down to the right?

What I mean is, if we are considering M^{*} \otimes M \otimes M^{*} which means M \times M^{*} \times M \rightarrow \mathbb{R}, so the argument is of the from (x,f,y) where f are linear forms, so since f are elements of M* and x,y is in M, then why don't we write M \otimes M^{*} \otimes M instead?

I've been looking through my notes for the last few weeks and i still do not see the reason for this use of notation that my lecturer uses, for example We denote by M^{*} \otimes M \otimes M^{*} the vector space of all tensors of type M \times M^{*} \times M \rightarrow \mathbb{R}, where M is...

Ah, damn it, I see it now it's a just a matter of doing a Taylor expansion! :smile: