# Some Features of Semiclassical Chiral Transport in Rotating Frames

## TL;DR

This paper develops a relativistic chiral transport theory in curved spacetime and rotating frames, deriving a new three-dimensional kinetic equation that accounts for electromagnetic fields, vorticity, and spatial dependence, consistent with known quantum anomalies.

## Contribution

It extends existing chiral kinetic theories to curved spacetime and rotating frames, providing a new 3D transport equation with explicit spatial dependence and anomaly consistency.

## Key findings

- Derived a relativistic chiral transport equation in curved spacetime.
- Established a nonrelativistic limit yielding a 3D kinetic theory.
- Confirmed consistency with chiral anomaly, magnetic, and vortical effects.

## Abstract

Semiclassical chiral kinetic theories in the presence of electromagnetic fields as well as vorticity can be constructed by means of some different relativistic or nonrelativistic approaches. To cover the noninertial features of rotating frames one can start from the modified quantum kinetic equation of Wigner function in Minkowski spacetime. It provides a relativistic chiral transport equation whose nonrelativistic limit yields a consistent three-dimensional kinetic theory which does not depend explicitly on spatial coordinates. Recently a chiral transport equation in curved spacetime has been proposed and its nonrelativistic limit in rotating coordinates was considered in the absence of electromagnetic fields. We show that the modified theory can be extended to curved spacetime. The related particle current density and chiral transport equation for an inertial observer in the rotating frame are derived. A novel three-dimensional chiral kinetic transport equation is established by inspecting the nonrelativistic limit of the curved spacetime approach in the rotating frame for a comoving observer in the presence of electromagnetic fields. It explicitly depends on spatial coordinates. We prove that it is consistent with the chiral anomaly, chiral magnetic and vortical effects.