Large Hardon Collider

[Kaylia]

Maybe I should have said size? This english/french thing is killing me, some wording are just plain different.

[edit]
http://en.wikipedia.org/wiki/Unitary_group
"The unitary group U(n) is a real Lie group of dimension n²"


It's basically what I'm trying to demonstrate. The follow up is a question that ask you to demonstrate that SU(n) (the sub-group of hermitian operator with a determinant=1) is n²-1


[edit]
What I wrote (until I find a better answer)

[Kaylia]

What I wrote so far, which isnt a formal proof (but its the best i can do)


For U(n):
A real n x n matrice has n orthogonal vector. Because unitary matrice are complex. R^n ⊗ C = R^n ⊗ R² = R^n²

SU
The constraint imposed by the determinant allow you to express any orthogonal vector with the combination of all other, lowering the degree of liberty by 1.

[Max™]

http://www.dailymail.co.uk/sciencete...#ixzz1Dxf8y19n

Scientists believe they may have found a new planet in the far reaches of the solar system, up to four times the mass of Jupiter.
Its orbit would be thousands of times further from the Sun than the Earth's - which could explain why it has so far remained undiscovered.
Data which could prove the existence of Tyche, a gas giant in the outer Oort Cloud, is set to be released later this year - although some believe proof has already been garnered by Nasa with its pace telescope, Wise, and is waiting to be pored over.

[Woozie]

Edit: An idiot I am. For a second I thought you meant the order of the group, but it doesn't seem like you are since the order would depend on the field. I'm still not understanding what you mean by dimension.

[Tyche]

http://www.dailymail.co.uk/sciencete...#ixzz1Dxf8y19n

I hope the pronounce my name correctly.

[Max™]

How optimistic of you.

[Kaylia]

Edit: An idiot I am. For a second I thought you meant the order of the group, but it doesn't seem like you are since the order would depend on the field. I'm still not understanding what you mean by dimension.

Hmm, do you understand what they mean by dimension here (6th lines)? http://en.wikipedia.org/wiki/Unitary_group

The way I understand it, a group of dimension n is the number of unique items required to describe every other items given a particular group operation (matrices multiplication).


U(n) is the unitary group and contains every unitary matrices (n² dimensions)
SU(n) is the special unitary group where the determinant of each matrix is 1 (n²-1 dimensions)

Pauli matrice are unitary, an similarly to SU, the determinant =-1. That's why we have 3 matrices instead of 4. (n²-1)

[Ferion]

I honestly don't really know that much (or anything) about unitary matrices and group theory, but to me Kaylia it sounds like what you're trying to describe as a "group dimension" is just the dimensions of a basis.

[Kaylia]

Well, I know it's the same (or similar), I'm just going with what is written in my book and everywhere else that talk about Lie-group.

[Woozie]

I guess I'll have to find my old Group Theory books from my topics class. I haven't even looked at lie groups since then and I still don't understand what dimension means (though I think we went over it in Topics).

[ZarakiKujata]

http://www.dailymail.co.uk/sciencete...#ixzz1Dxf8y19n

haha I came to this thread just to post that story.

Grats on your new fame Tyche.

[Mizango]

haha I came to this thread just to post that story.

Grats on your new fame Tyche.

Hooooly cow.

[Woozie]

Tyche is too skinny to be called a cow, let alone a holy one.

[Tyche]

I think I need a new catchy title.

[Kaylia]

I guess I'll have to find my old Group Theory books from my topics class. I haven't even looked at lie groups since then and I still don't understand what dimension means (though I think we went over it in Topics).

Don't worry about it. I needed that for a presentation yesterday, but its over already.

[Dimmauk]

haha I came to this thread just to post that story.

Grats on your new fame Tyche.

I just read about this, and LOL'd at the name.

I never knew Tyche was from Oort.

[Eliseos]

Probably dropping quantum mechanics II because

a) It isn't required by my dual major

b) It is absolutely uninteresting to me, whereas the first semester was semi-interesting (and also required).

c) I wouldn't have to be to school on Tuesday/Thursdays until 2PM

d) I don't want to do all that much work in my last semester as an undergrad.

Also yay @ potential new planet.

[Woozie]

Don't worry about it. I needed that for a presentation yesterday, but its over already.

Was you presentation on Lie Groups in physics? I did a presentation on Lie Group representations in physics last year and I probably could have dug it up if I had known it was for that. Assuming it's on this computer and not my broken computer.

Edit: Eli, what's covered in QMII? The only thing in QM that isn't very interesting is approximation methods (though incredibly useful for physicists) and any applications to chemistry.

[Eliseos]

Both time-independent and dependent perturbation theory, variational principle, WKB approximation. Pretty much all approximation methods. I get why physicists need to use it, I just don't very much like it and haven't really had an interest in it this entire semester. If I was planning, or thought considerably about pursuing physics in graduate school I'd stay in the class, but I'm 99% sure I will pursue something in engineering for my graduate studies, whenever I get there.

[Kaylia]

Was you presentation on Lie Groups in physics? I did a presentation on Lie Group representations in physics last year and I probably could have dug it up if I had known it was for that. Assuming it's on this computer and not my broken computer.

Edit: Eli, what's covered in QMII? The only thing in QM that isn't very interesting is approximation methods (though incredibly useful for physicists) and any applications to chemistry.

More or less. We have 4 questions to solve every week, but only present one out of the four (since we don't know which one we will get, we have to be ready for everything). We were asked to be as rigorous as possible, and demonstrate everything (starting from the most basic axioms usually). One of the questions involved the proof I asked for, but that's not what I got this time (I got worse, it was another one I wasnt able to solve at all >_>).

[edit]
Even if this chapter is over, I would be interested to see what you wrote. More information can't hurt since there is a lot I dont understand.