Understand
We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-$\frac12$ particle with definite helicity.
- We find that the ordinary Lorentz transformation is modified by a shift orthogonal to the boost vector and the particle momentum.
- The shift ensures angular momentum conservation in particle collisions and implies a nonlocality of the collision term in the Lorentz-invariant kinetic theory due to side jumps.
- We show that 2/3 of the chiral-vortical effect for a uniformly rotating particle distribution can be attributed to the magnetic moment coupling required by the Lorentz invariance.
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