Recent content by timb00

Hi, thank you quasar987 and dextercioby for your replay. I will have a look on the sources you recommended to me. Till now I only though about it using Dynkin diagrams. Maybe a last question. If u is an element of the lie algebra of U(n), say an n x n skew hermitian matrix. Exist there an...

Hi everybody, I hope that I chose the right Forum for my question. As the title might suggest, I am interested in the embedding of the Lie algebra of U(n) into the Lie Algebra of O(2n). In connection with this it would be interesting to understand the resulting embedding of U(n) in O(2n). I...

Thank you for your fast answers. They have confirmed my expectancy. I ask this question because I am concerned with invariant theory and statistical physics. I learned that every polynominal function that is invariant under the action of a Lie group is a pull back of a function on some matrix...

Hey everybody, I have a short question. Suppose you have an analytic function f(z) such that you can, at least locally, expand it in a power series. Is this function then (locally) an element of the algebra of polynominals in z? I hope I formulate the question in the right way. Best...

Hey everybody, I have to give a talk in our seminar on invariant theory of Lie Groups. And I'm now looking for easy applications of invariant theory to quantum physics. I want to present them to motivate the discussion. I would be lucky if someone of you has an idea where I can found...

I agree with you in this point, I think the problem is that no compactification mechanism is used, so that this model Lagrangian is just a effective description of theory which is spontaneously broken at the Planck scale. The question which bothers me is why do they occur when the...

Thx suprised for your answer. The model has a scale which is 1/R. An effective action in a regime of E << 1/R would only consist of the zero modes of the fields with positive parity. I'm not sure about the symmetry above the breaking scale, but I think it could be restored either...

Hi, I am interested in grand unification with extra dimensions. Especially the case when extra dimensions are broken by orbifolding. Now I am trying to understand how the Goldstonebosons appear in the spectrum of a theory with global (for example SU(N)) symmetry. From the...

Hi how, in my master project I am working on extra dimensions and I am asking my self why is it common to start most of the theories with a space time symmetry given by SO(n,1) (n>4) and then compactify the obtained spectrum to SO(3,1)xG (where G is an abitrary symmetry group). Because...

Hi Bill_K, and sorry for my late replay. I'm not quite sure why we are using the 15+1. I had a very long discussion with my Professor and my second supervisor About that, and I'm not familiar with the Higgs breaking scheme because the main part of my work is on Orbifold breaking an Extra...

Hi Bill_k, It actually has, because if your write the 15 as 15 = \begin{pmatrix}8 & 3 \\ \bar 3 & 1 \end{pmatrix} they will appear, e.f. Tr(15^2)^2 = (Tr(8^2) +2~3\bar3 + 1^2)^2 =Tr(8^2)^2 + 4~Tr(8^2) 3\bar3 + 2 Tr(8^2) ~1^2 + 2~3\bar3~1^2 + 1^4 +4~(3\bar3)^2. This is due to the...

Hello everybody , and first of all thanks four reading to everybody and a thank you Bill_K for your reply. I think all your remarks where right. Yesterday I found a dissertation where they gave an example of a Higgs potential. In this paper they used for every term of the potential a...

Hi guy's, this is my first thread at Physics-forums. I am currently working on GUT's and try to learn the Higgs mechanism. Therefore my supervisor gave me a toy model. This model is a SU(4) gauge theory with a infinite series of 4+ \bar 4 as Matter fields (fermions) and a Higgs sector which...

Hey Guy's, thanks for reading my thread. I found my mistake. It was just the wrong normalization. If someone is interested I will make a sketch how I compute the weight projector. For the A_2 I take the Cartan sub algebra to be generated out of {a'1,a'2}={4/3*a2,4/3*ax}. The factor of 4/3...

Hello everybody, this is the first thread of mine. I try to recover the decomposition of the fundamental representation (the 7) of G2 into irreducible representations of A_2. It is given by 7 = 3 + [tex]\bar {3}[\tex] + 1 It maid be that I didn't understand the procedure, founded...