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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 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
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
correction to the distribution function in each
reference frame
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