Operators that are associated with several important quantities, such as angular momentum, play a double role: they are both generators of the symmetry group and ``observables.'' The analysis of different splittings of angular momentum into ``spin'' and ``orbital'' parts reveals the difference between these two roles. We also discuss a relation of different choices of spin observables to the violation of Bell inequalities.
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Daniel R. Terno (2003) studied this question.
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