Lorentz Invariance in Chiral Kinetic Theory

TL;DR

This paper demonstrates how Lorentz invariance manifests nontrivially in the classical action of massless chiral particles, affecting collision dynamics and contributing to the chiral-vortical effect.

Contribution

It reveals a modified Lorentz transformation with a shift orthogonal to momentum, ensuring angular momentum conservation and explaining part of the chiral-vortical effect.

Findings

Lorentz invariance involves a nonlocal shift in particle trajectories.

The shift ensures angular momentum conservation in collisions.

Two-thirds of the chiral-vortical effect is due to magnetic moment coupling.

Abstract

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. We also show how the classical action can be obtained by taking the classical limit of the path integral for a Weyl particle.