https://arxiv.org/abs/0811.2190
I'm George, not Adolfo. By the sounds of it you're more general and abstract than my approach.
We came to the problem by selecting an orientifold in string theory with a particular symmetry, an isotropic 6d torus - this meant all structure constants must have...
Wow, you found a post from... (checks date) 11.5 years ago.
Thanks for the reply regardless. Just so you know, there is an algorithmic way to do it IF you know the specific set of Lie algebras f and g can be the structure constants of but it's highly non-trivial - in the case I was interested...
1) There's an obvious collection of 'good places' and 'bad'. The difference between say Oxford and Cambridge will depend quite a bit on what you will be doing specifically, 6 of one, half a dozen of the other. There's an across the board difference between say Imperial and Aston. If you're...
If you can get a high distinction in your 4th year then it's a demonstration you understand the relevant 1st year material pretty well. After all, you cannot do 4th year GR if you don't know what a gradient from 1st year vector calc is.
The way the Cambridge maths (and I think physics) degrees...
I have a few friends doing Cambridge PhDs in maths and physics. About 80% of them got high 1st all the way through uni. The other 20% are a mixture of steadily improving through the years from say a bad 3rd the Christmas in 1st year up to a top 10 in 4th year along with bad 3rds and 2.2s up...
I have two Lie algebras with structure constants f^{a}_{bc} and g^{a}_{bc}, the number of generators being the same (as will become clear).
Due to a particular symmetry/construct, I have that the system needs to be valid under g \to af + bg (and a similar transform for g), which leads...
That is only true if your metric is Lorentzian. If your metric has 2 time-like directions then you can go up to D=12, as is done in F theory. I think beyond that you cannot get spin=<2 only, no matter how many time-like dimensions you have.
Can you please be more specific about which section? I...
^ Definitely. If you're not familiar with quantum field theory (and very few universities do it before the 4th year) then much of string theory is going to be lost on you. Stuff like Lie algebras is in a similar vein, the details of them aren't often taught to undergrads (I'm not counting a 4th...
I assumed that the matrices are 2x2, so I guess that refers to them being diagonalisable as a Real matrix. Unfortunately I don't have access to this book, he asked me over the phone and what he said differed a few times from what he then emailed me. I assume he's quoting directly, but that might...
My dad came across this phrase in a book but neither of us are familiar with it. The statement is :
"Let M_{1} and M_{2} be matrices. N = M_{1}^{-1}M_{2}. This matrix is M_{1} symmetric and so it diagonalisable in \mathbb{R}^{2}."
Does it just mean that M_{1}=M_{1}^{T} or something else...
You're confusing the sci-fi notion of 'extra dimensions' with the physics notion of 'extra dimensions'.
In sci-fi, when they say "The 5th dimension" or "Another dimension", they generally mean a parallel universe. In physics, this isn't the same. Extra dimensions are basically 'extra...
Isn't this a bit like (but obviously much more complicated) that puzzle which is a 4x4 grid of 15 slidable tiles with 1 'gap'. The puzzle is to slide them around so that they are in order (like on a keyboard's number pad). Not all initial configurations can be solved. For instance, if you have...