18
votes
6answers
858 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
354 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
339 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 $(2,0)$?