Zilch Vortical Effect for Fermions

TL;DR

This paper introduces a fermionic zilch current as an analog to the photon zilch, demonstrating its conservation and a vortical effect in rotating media, expanding the understanding of chiral effects related to particle spin.

Contribution

It generalizes the concept of zilch from photons to fermions, defining a conserved fermionic zilch and revealing its vortical effect in rotating media.

Findings

Fermionic zilch is conserved in non-interacting theory.

Fermionic zilch exhibits a vortical effect in rotating media.

The results extend chiral effects to include particle spin considerations.

Abstract

We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start with the definition of the photonic zilch current in chiral kinetic theory framework and work out field-theoretical definition of the fermionic zilch using the Wigner function formalism. This object has similar properties to the photonic zilch and is conserved in the non-interacting theory. We also show that, in full analogy with a case of photons, the fermionic zilch acquires a non-trivial contribution due to the medium rotation - zilch vortical effect (ZVE) for fermions. Combined with a previously studied ZVE for photons, these results form a wider set of chiral effects parameterized by the spin of the particles and the spin of the current. We briefly discuss the origin of the ZVE, its possible relation to the anomalies in the underlying microscopic theory and possible application for studying the spin polarization in chiral media.