Recent content by spookyfish

I have seen the following textbook: "A Modern Introduction To Particle Physics" by Fayyazuddin https://www.amazon.com/dp/9814338834/?tag=pfamazon01-20 I couldn't find reviews in Amazon, and I have seen only one review in google books that claimed that the book had errors, but did not give...

Hi. Thank you very much! This is exactly what I was looking for. the explanation is very clear. I only have one question (that I think does not affect the proof): Why did you assume that U is given in the fundamental representation U=1+i\omega^aT_F^a

I understand. But I don't see how this transformation rule is consistent with the definition I know of the adjoint rep: Is it possible to assume that T transforms as GT_a G^{-1} and then prove that it is given by the adjoint representation [T_a]_{bc}=-if_{abc} ? where f_{abc} are determined...

How can you see that?

A gauge field W_\mu is known to transform as W_\mu\to W'_\mu=UW_\mu U^{-1} +(\partial_\mu U)U^{-1} under a gauge transformation U, where the first term UW_\mu U^{-1} means it transforms under the adjoint representation. Can anyone explain to me why it means a transformation under the adjoint...

Thank you. you are right, it works out! I stopped when I didn't understand this line, which is a typo, and should have continued in the first place

Yes. Sorry, I am using the following reference: http://www.damtp.cam.ac.uk/user/ho/GNotes.pdf and trying to fill in the gaps. This is at the end of page 41, and on page 42. My problem is the top of eq. (4.30) given the definition (4.29).

Yes. I used it, and I am pretty sure it leads to \Lambda = 1+ [\omega_2,\omega_1] . I am not sure then how it would lead to U(1+[\omega_2,\omega_1])=1-i[\omega_2,\omega_1]^{\mu \nu} M_{\mu \nu} (there is a missing factor 1/2 according to my convention)

yes.

I am trying to derive the algebra and I get a factor of 2 wrong... Consider the Lorentz group elements near the identity \Lambda_1^\mu\,_\nu = \delta^\mu\,_\nu + \omega_1^\mu\,_\nu, \quad \Lambda_2^\mu\,_\nu = \delta^\mu\,_\nu + \omega_2^\mu\,_\nu and write a representation as...

Fine, but that still does not answer my question. I will appreciate if someone will be able to take the time and try to answer my previous question.

Unfortunately that was not my question. I know that states are vectors. My question was - why finding vectors and not the matrices? I thought that our goal in representation theory was to find matrix representations of groups

Why are the states as useful in describing the group structure as the matrices themselves? is it because it easy to build the matrices from the states (using weights and roots)?

Thanks. That answers my second question, i.e. connect the tensors to the state representations. So the irreducible representations are represented by symmetric and antisymmetric tensors. But I still don't know why this is true. I read that in general the irreps of SU(N) are tensors with definite...

I know the connection to states: the LHS is the direct product of 2D states and the RHS is the 3D and 1D states corresponding to the irreps.