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 $\widehat{\mathbf{O}}(\hslash )$ 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 $\widehat{\mathbf{O}}(\hslash )$ correction to the distribution function in each reference frame.

• Received 2 February 2018

DOI:https://doi.org/10.1103/PhysRevD.98.036010

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Published by the American Physical Society