  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.

High Energy Physics - Theory;High Energy Physics - Phenomenology;Nuclear Theory