Space Rotations and Angular Momentum

In this chapter the orbital angular momentum will be introduced as the generator of the space rotations. Since rotations are a non-commutating (non-Abelian) group, the components of the orbital angular momentum are not simultaneously measurable in quantum mechanics, at variance with classical mechanics. The spin will also be introduced as generator of the SU(2) transformations in intrinsic space, with the same algebraic properties as the angular momentumAngular momentum. The coupling of angular momentum with spin raises the issue of extending the symmetries of physical systems under rotations to more general transformations.