I know that the generators of the Poncaire group that are associated with *orbital* angular momentum belong to an infinite dimensional representation, i.e.(adsbygoogle = window.adsbygoogle || []).push({});

\begin{equation}

L = \frac{\partial}{\partial \theta}

\end{equation}

Also the spin generators are associated with some finite dimensional representation of a lie algebra (such as the fundamental rep of SU(2) for spin 1/2 particles). Both of the groups commute with one another and should have their own symmetry charges.

Now my question is, in spin orbit coupling why is it L+S which is the conserved quantity and not L and S separately?

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# Symmetries and Spin orbit interaction

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