Disentangling covariant Wigner functions for chiral fermions

Understand

We develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant $\hbar$.

• We demonstrate to any order of $\hbar$ that only the time-component of the Wigner function is independent while other components are explicit derivative.
• We further demonstrate to any order of $\hbar$ that a system of quantum kinetic equations for multiple-components of Wigner functions can be reduced to one chiral kinetic equation involving only the single-component distribution function.
• These are remarkable properties of the quantum kinetics of chiral fermions and will significantly simplify the description and simulation of chiral effects in heavy ion collisions and Dirac/Weyl semimetals.