Representations of the three-dimensional rotation group by the direct method
A. J. Torruella · Journal of Mathematical Physics · 1975
The irreducible representations of the three-dimensional rotation group are obtained directly from the irreducible representations of its infinitesimal generators (the spin matrices), parametrized in terms of the rotation angle and the direction of the rotation axis. Expressions are given for the rotation operator exp(iψn ⋅ S) in terms of two different bases of 2j+1 elements for spin j. The results are related to the spectral decomposition of the rotation operator and expressions obtained for spin projection operators along any spatial direction for arbitrary spin.