The Dirac equation for a free particle reads
H = c*alpha*p + beta*m*c^2
(Sorry for the miserable formatting - how to enter Latex Code or similar?)
The commutator [H,L_i] is nonzero for any component, which is amended by introducing the spin.
But what nags me is the fact that the orbital angular momentum, without any interaction, is not conserved. How can this be interpreted? What does the particle do? It should not change its direction just like that, should it?
Thanks in advance
This is an inteligent question.
As you may know, spin in relativistic QM comes out naturally from the theory,
and does not have to be added as a separate term, like in nonrelativistic QM
So from this point of view, spin is a relativistic effect, so it cannot be left out.
Of course this answer is not that intuitive, sorry about that. One could hope for a better answer, that I do not have now.
The only other possible answer would be dissapointing, that Dirac is flawed,
similar to the velocity disaster that some seem to believe in.
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