18
votes
5answers
680 views

Tensor Operators

Motivation. I was recently reviewing the section 3.10 in Sakurai's quantum mechanics in which he discusses tensor operators, and I was left desiring a more mathematically general/precise discussion. ...
2
votes
1answer
319 views

Eigenvectors of a 4D rotation, and their interpretation

Let us define a 4D rotation by using two unit quaternions: $$\mathring{q}_l=\frac{a+ib+jc+kd}{\left|a+ib+jc+kd\right|}$$ and $$\mathring{q}_r=\frac{e+ib+jc+kd}{\left|e+ib+jc+kd\right|}.$$ They differ ...
3
votes
1answer
289 views

How do I find the tensor components of all weights of a representation of SU(3), e.g. the six dimensional representation (2,0)

How do I find the corresponding tensor component v^ij of the six dimensional representation of SU(3) with dynkin label (2,0).