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.
Highlights
The many-body physics of massless fermions has attracted significant interest in a wide range of communities, from condensed matter physics to high-energy heavy ion collisions
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 OðħÞ order
A detailed proof is given for the general and unique solution of the peculiar component Kμ in the OðħÞ-order chiral component of the Wigner function. This new analysis clarifies exactly why and how the Lorentz-invariance and frame-dependence issues associated with the OðħÞ correction to the phase space distribution function arise within a totally covariant framework
Summary
The many-body physics of massless fermions has attracted significant interest in a wide range of communities, from condensed matter physics to high-energy heavy ion collisions. A natural approach is to derive the quantum transport equation for chiral fermions in the well-known Wigner function formalism by a systematic semiclassical expansion in terms of ħ [51,52,53,54,55,56] We shall adopt this approach in the present paper. A covariant set of chiral transport equations to ħ order This detailed derivation will allow a clear understanding, within a totally covariant framework, of the origin for the rather confusing Lorentz-invariance and framedependence issues as well as the emergence of the Berry phase, Berry curvature and anomalous terms in the 3D formulation of chiral kinetic theory. An Appendix is included to prove in great technical details the completeness and uniqueness of the found OðħÞ solution to the constraint equations, which is crucial for understanding the frame-dependence issue
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