Complete and Consistent Chiral Transport from Wigner Function Formalism

TL;DR

This paper derives a comprehensive covariant chiral transport equation for massless fermions using Wigner function formalism, resolving issues of Lorentz invariance and frame dependence at the semiclassical level.

Contribution

It provides the first complete and consistent semiclassical solution to covariant chiral transport equations, clarifying frame dependence and Lorentz invariance issues.

Findings

Resolved frame dependence in chiral kinetic theory.

Established a unique definition of $oldsymbol{ ext{O}( ext{hbar})}$ corrections.

Proved Lorentz invariance of the covariant transport equations.

Abstract

Recently there has been significant interest in understanding the macroscopic quantum transport in a many-body system of chiral fermions. A natural framework for describing such a system which is generally out of equilibrium, is the transport equation for its phase space distribution function. In this paper, we obtain a complete solution of the covariant chiral transport for massless fermions, by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion up to $\hat{\mathbf{O}}(\hbar)$ order. In particular, we clarify certain subtle and confusing issues surrounding the Lorentz non-invariance and frame dependence associated with the 3D chiral kinetic theory. We prove that such frame dependence is uniquely and completely fixed by an unambiguous definition of the $\hat{\mathbf{O}}(\hbar)$ correction to the distribution function in each reference frame.