Well I can see no response then I shall rephrase the question.
Is it true, and if so why is it true, that the groups A(N-1) and SU(N) have the same root system? i.e. Isomorphic algebras? What is the appropriate group morphism? etc.
According to this book I'm reading these groups are said to be equivalent and I am trying to better understand how this is so.
The generators of SU(N) are N^2-1 traceless complex anti-hermitian matrices. The group is over the real numbers and is N^2-1 dimensional.
On the other hand we have...
Hi,
I don't think this belongs in the homework section since this is a graduate course.
My question is regarding making a field theory generally covariant by including a metric tensor g_{\mu\nu}(x)in the Lagransian density, and it's transformation under infinitesimal coordinate change...
They didn't hire me yet:smile: .
A lot of the techniques in Quantum Field Theory apply to solid state physics too, so it's not that far fetched. I chose string theory because it's interseting and hard, probably wasn't the smartest career move though.
They didn't tell me, but I'm guessing...
Hi,
I'm finishing my M.Sc. degree in physics, my focus being on string theory, and I have an interview with Intel in 3 weeks. The position involves improving the efficiency and performance of their microprocessor chips. I want to come to the inerview prepared.
I know a lot about Quantum...
You are right Matthew the f's and u's have some very neat properties which I left out because a lot of mathematicians are not familiar with the Minkovsky product which is the appropriate product for unified space time. Let's denote it by star, such that...
Yes but what is your ruler? The only "ruler" available to you is other particles, via collision experiments. If extra dimentions exsits then they would affect your ruler as well as the so called extra dimention you are trying to measure, so this problem is not at all trivial.
Also the lack of...
Not really
There are 3 equations for each component of \vec{U}(x) since the index i goes between 1..3. For example the first equation can be explicitly written as:
U_1^{'}(x)=c(f_1(x)-U_1(f_1 U_1+f_2 U_2+f_3 U_3))
As for the unknows, that doesn't mean you can't formulate a general solution...
Extra Dimentions
As far as I understand it the extra dimentions in string theory arise when you go from the a the classic description of string theory to the quantum description. It comes about because the theory must obey certain symmetry principles which force higher dimentions into the...
Hi,
I'm looking for an analytical solution to this set of coupled equations:
U^{'}_{i}(x)=c (f_i(x)-(\vec{U}\cdot\vec{f})U_i(x))
Where the vectors are 3 dimentional, c is constant and f is a vector of given functions:
f_i(x) , i\in 1..3
There probably isn't one but I thought I'd...