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.
Highlights
In the presence of external electromagnetic fields the charged, massless Dirac particles which can be right- or left-handed, exhibit unusual features like the chiral magnetic effect [1,2,3] and the chiral separation effect [4,5]
To have better insights into the transport properties of particles, it is convenient to consider the 3D chiral kinetic theory (CKT) generated by the relativistic chiral transport equation (CTE)
The CKT which follows possesses x dependent terms and resembles the one established in [16]. We show that it is consistent with the chiral anomaly, the chiral vortical and magnetic effects
Summary
In the presence of external electromagnetic fields the charged, massless Dirac particles which can be right- or left-handed, exhibit unusual features like the chiral magnetic effect [1,2,3] and the chiral separation effect [4,5]. A relativistic chiral kinetic theory (CKT) can be defined [17,18,19] starting from the quantum kinetic equation (QKE) obeyed by the Wigner function [20,21] It does not take into account all noninertial effects like the Coriolis force. To have better insights into the transport properties of particles, it is convenient to consider the 3D CKT generated by the relativistic chiral transport equation (CTE) This limit is challenging, the nonrelativistic CKT should be consistent with chiral anomaly and anomalous currents. The nonrelativistic limit in the absence of electromagnetic fields was discussed for two different choices of four-velocities corresponding to inertial and rotating observers For the latter choice the CTE which they obtained is the same with the one derived in [16] at x ≈ 0. In the last section the results acquired and future directions are discussed
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