Classical chiral kinetic theory and anomalies in even space-time dimensions

Abstract

We propose a classical action for the motion of massless Weyl fermions in a background gauge field in (2N + 1) + 1 spacetime dimensions. We use this action to derive the collisionless Boltzmann equation for a gas of such particles, and show how classical versions of the gauge and Abelian chiral anomalies arise from the Chern character of the non-Abelian Berry connection that parallel transports the spin degree of freedom in momentum space.

A semiclassical formulation of the chiral magnetic effect and chiral anomaly in even d + 1 dimensions

“…The main novelty is to keep the spin dependence explicit without attributing them some dynamical variables. It seems that there is no obstacle of incorporating external non-Abelian gauge fields to our method in the line with [13,21].…”

“…On the other hand, it is possible to deal with matrix valued Hamiltonians in the presence of the Berry gauge fields systematically [14]. Inspired with this approach, though following mainly the differential form methods employed in [13], we present a formalism of the classical chiral kinetic theory in even d + 1 dimensions yielding both the chiral anomaly and chiral magnetic effect in external electromagnetic fields. We also show that the chiral vortical effec!…”

Electromagnetic fields and anomalous transports in heavy-ion collisions—a pedagogical review

“…There are a variety of methods to derive Eq. (30) from microscopic quantum field theory [2, 15, 102-104, 115, 117, 119, 120, 136, 137], mesoscopic kinetic theory [138][139][140][141][142][143][144][145][146][147][148][149][150][151][152], to macroscopic hydrodynamic approach [22,[153][154][155][156][157][158]. Here we pick up one of these derivations given by Fukushima, Kharzeev, and Warringa [115] because it is elementary and easy to see the relation between CME and the lowest Landau level and the axial anomaly.…”

Chiral kinetic theory and anomalous hydrodynamics in even spacetime dimensions

“…Subsequently, their computation was generalized to nonabelian gauge anomalies [17] in arbitrary even spacetime dimensions [18] by constructing an anomalous symplectic form on an extended phase space, where the anomaly signals a breakdown of the Liouville's theorem. The formalism has also been used to describe the transport processes associated with gauge anomalies, for instance, the chiral magnetic effect(CME) and chiral vortical effect(CVE) [15,16].…”

“…18. In Sec III, we review the basics of relativistic hydrodynamics, including the differential form notation proposed in Ref.…”