Recent content by nigelscott

I am looking at this document I do not understand how the author gets 5.12 and 5.13 on page 133. I think the matrix of partials should be the transpose of the one shown. Even so I still can't figure out how you get 5.13. Any help would be appreciated.

I am looking at the representation of D4 in ℝ4 consisting of the eight 4 x 4 matrices acting on the 4 vertices of the square a ≡ 1, b ≡ 2, c ≡ 3 and d ≡ 4. I have proven that the 1-dimensional subspace of D4 in ℝ2 has no proper invariant subspaces and therefore is reducible. I did this in 2...

OK. Thanks to you both. I think I understand it now.

Ok. Thanks for your response. The example I am using is from this video here starting at 12 mins and continuing here. Here he talks about tangents to the sphere with the Lie bracket being another tangent to the sphere which is at odds with the cross product which would produce a vector normal...

Prove that for a 2 sphere in R3 the Lie bracket is the same as the cross product using the vector: X = (y,-x,0); Y = (0,z-y) [X,Y] = JYX - JXY where the J's are the Jacobean matrices. I computed JYX - JXY to get (-z,0,x). I computed (y,-x,0) ^ (0,z,-y) and obtained (xy,y2,yz) = (z,0,x)...

This will take me a little time to digest, but in the meantime I wanted to thank everyone for your responses.

OK. Thanks. It seems that this involves numerical analysis and is best solved using MATLAB etc. Is that a fair assessment?

How does one go about finding a matrix, U, such that U-1D(g)U produces a block diagonal matrix for all g in G? For example, I am trying to figure out how the matrix (7) on page 4 of this document is obtained.

I am looking at page 2 of this document.https://ocw.mit.edu/courses/chemistry/5-04-principles-of-inorganic-chemistry-ii-fall-2008/lecture-notes/Lecture_3.pdf How is the transformation matrix, ν, obtained? I am familiar with diagonalization of a matrix, M, where D = S-1MS and the columns of S...

Perfect. Thank you!

Hello. I just came across this post. I understand how the 2nd term in (4) is to equivalent to the 1st term in the 1st equation i.e. uivjk - ujvik = εijlεlmnunvmk = (δimδjn - δjnδim)umvnk but I am having a mental block regarding how the first term in (4) is equivalent to the 2nd term in the...

Yes, I am familiar and recognize that Young tableaux is easier for practical purposes. However, this approach should give the same result, yes?

SU(3).

Thanks. Yes, I am familiar with using the ladder operators. I was more focused on the procedure outlined using the 3 ⊗ 8 by Georgi (LIe Algebras in Particle Physics page 143) and also here https://physics.stackexchange.com/questions/102554/tensor-decomposition-under-mathrmsu3 . I was trying...

Homework Statement [/B] I am trying to get the C-G Decomposition for 6 ⊗ 3. 2. Homework Equations Neglecting coefficients a tensor can be decomposed into a symmetric part and an antisymmetric part. For the 6 ⊗ 3 = (2,0) ⊗ (1,0) this is: Tij ⊗ Tk = Qijk = (Q{ij}k + Q{ji}k) + (Q[ij]k +...