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[tex][J_i,J_j] = \sum_k \epsilon_{ijk} J_k[/tex]

and

[tex][L_i,L_j] = \sum_k \epsilon_{ijk} L_k[/tex]

1st question, I am right in thinking that [tex]J[/tex] represents Eingavalues for spin 1/2 particles... next...

Computing the commutation relations, I find that

[tex]\sum_k \epsilon_{ijk} (J_K + L_K - L_k - L_k)[/tex]

collapses to simply

[tex]\sum_k \epsilon_{ijk} S_k[/tex]

because [tex]S_i \equiv J_i - L_i[/tex]

2nd question: Now, I believe that taking such a difference means the total angular momentum and the orbital angular momentum just means that [tex]S_i[/tex] will become the generator of rotations for a particle around it's own axis which means we won't be moving the object in this expression... is this right?

3rd question, is [tex]S[/tex] simply the rotational spin say possibly describing a sphere?

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# Generator of Rotations and commutation relationships

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