Semiclassical dynamics of Dirac and Weyl particles in rotating coordinates

TL;DR

This paper develops a semiclassical kinetic theory for Dirac and Weyl particles in rotating frames with electromagnetic fields, revealing their phase-space dynamics and anomalous chiral effects.

Contribution

It introduces a Hamiltonian formulation using a symplectic two-form for Dirac particles and extends the theory to Weyl particles, linking their phase-space dynamics.

Findings

Derived particle number and current densities in the helicity basis.

Calculated anomalous chiral effects due to electromagnetic fields and rotation.

Established the connection between Dirac and Weyl particle dynamics.

Abstract

The semiclassical kinetic theory of Dirac particles in the presence of external electromagnetic fields and global rotation is established. To provide the Hamiltonian formulation of Dirac particles a symplectic two-form which is a matrix in spin indices is proposed. The particle number and current densities for the Dirac particles are acquired in the helicity basis. Following a similar procedure, semiclassical kinetic theory of the Weyl particles is accomplished. It is shown that the phase-space dynamics of the Weyl and Dirac particles is directly linked. The anomalous chiral effects due to the external electromagnetic fields and angular velocity of the frame are calculated.