Relativistic Chiral Kinetic Theory from Quantum Field Theories

TL;DR

This paper derives a relativistic chiral kinetic theory for Weyl fermions from quantum field theories, highlighting the importance of side-jump effects and Lorentz symmetry breaking in the presence of electromagnetic fields and collisions.

Contribution

It introduces a derivation of chiral kinetic theory incorporating side-jump phenomena and Lorentz symmetry breaking from quantum field theoretical principles.

Findings

Side-jump terms significantly affect the derivation.

Lorentz symmetry is broken for distribution functions.

Modified Lorentz transformations are derived due to background fields and collisions.

Abstract

The chiral kinetic theory of Weyl fermions with collisions in the presence of weak electric and magnetic fields is derived from quantum field theories. It is found that the side-jump terms in the perturbative solution of Wigner functions play a significant role for the derivation. Moreover, such terms manifest the breaking of Lorentz symmetry for distribution functions. The Lorentz covariance of Wigner functions thus leads to modified Lorentz transformation associated with side-jump phenomena further influenced by background fields and collisions.