Boost invariant formulation of the chiral kinetic theory

We formulate the chiral kinetic equation with the longitudinal boost invariance. We particularly focus on the physical interpretation of the particle number conservation. There appear two terms associated with the expansion, which did not exist in the nonchiral kinetic equation. One is a contribution to the transverse current arising from the side-jump effect, and the other is a change in the density whose flow makes the longitudinal current. We point out a characteristic pattern in the transverse current driven by the expansion, which we call the chiral circular displacement.

Figure 1

Schematic figure to explain how the shift takes place.

Figure 2

Schematic figure to show the characteristic shift pattern seen from the transverse plane for $z>0$.