Lorentz Invariance in Chiral Kinetic Theory

Abstract

We show that Lorentz invariance is realized nontrivially in the classical action of a massless spin-$\frac{1}{2}$ 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.

5 pages, 1 figure

References in corpus (2)

• The Chiral Magnetic Effect
• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

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• Position, spin and orbital angular momentum of a relativistic electron
• Collective Modes of Chiral Kinetic Theory in Magnetic Field
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• Recent developments in chiral and spin polarization effects in heavy-ion collisions
• Anomalous Hall effects beyond Berry magnetic fields in a Weyl metal phase
• Conformal symmetry, chiral fermions and semiclassical approximation
• Microscopic Study of Vorticities in Relativistic Chiral Fermions
• World-line formulation of chiral kinetic theory in topological background gauge fields
• Anomalous Hall Effect for semiclassical chiral fermions