Anatomy of the chiral vortical effect

TL;DR

This paper investigates the chiral vortical effect in rotating relativistic fermions, comparing boundary condition solutions with topological invariant approaches to understand axial current generation.

Contribution

It introduces a novel comparison between boundary condition solutions and topological methods for calculating the axial current in rotating fermion systems.

Findings

Axial current calculated via Dirac equation with boundary conditions.

Relation of axial current to topological invariants in momentum space.

Consistency between different approaches to the chiral vortical effect.

Abstract

We consider the system of relativistic rotating fermions in the presence of rotation. The rotation is set up as an enhancement of the angular momentum. In this approach the angular velocity for the angular momentum plays the same role as the chemical potential for density. We calculate the axial current using the direct solutions of the Dirac equation with the MIT bag boundary conditions. Next, we consider the alternative way of the rotation description, in which the local velocity of the substance multiplied by the chemical potential serves as the effective gauge field. In this approach this is possible to relate the axial current of the chiral vortical effect for the massless fermions to the topological invariant in momentum space, which is robust to the introduction of interactions. We compare the results for the axial current obtained using the two above mentioned approaches.