Thank you. How do you see the geometrical meaning of the expression \exp(-\mathrm{i} \vec{\sigma} \cdot \vec{\varphi}/2? i.e. how do you see that it means a rotation at an angle \varphi about the axis \hat{\varphi} ? I thought about showing that the rotation matrix doesn't change the axis...
I see. Thank you
Ok. And \hat n parametrizes it since it can include any (normalized) 3d vector, thus describing any linear combination, and we can choose it to be normalized since a multiplicative factor in the exponent doesn't matter. Is that correct?
Hi. I know that the \sigma matrices are the generators of the rotations in su(2) space. They satisfy
[\sigma_i,\sigma_j]=2i\epsilon_{ijk}\sigma_k It is conventional therefore to take J_i=\frac{1}{2}\sigma_i such that [J_i,J_j]=i\epsilon_{ijk}\sigma_k . Isn't there a problem by taking these...