## Complete and consistent chiral transport from Wigner function formalism

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 that 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 noninvariance and frame dependence associated with the three-dimensional 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.

Publication Date:
Aug 15 2018
Date Submitted:
Jun 28 2019
Citation:
Physical Review D
98
3
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