Operators commuting with the Dirac operator

We write the Dirac operator in polar coordinates. Using (103) and (104) we obtain 

Here we have introduced the spin-orbit operator 

The operator K describes the part of the Dirac operator that acts on the angular variables. All other summands in (106) obviously only affect the radial variable r of a wave function. 

It appears not very sensible to extract the Dirac matrix (3 from the definition of K. The reason is that the operator K obtained in this way commutes with the Dirac operator Hq. In order to see this, we compute the eommutator 

Thus the operator 2S L +1 anticommutes with a tr. As the Dirac matrix (3 also anticommutes with a Cr we conclude that 

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