Consistent relativistic chiral kinetic theory: A derivation from on-shell effective field theory

We formulate the on-shell effective field theory (OSEFT) in an arbitrary frame and study its reparametrization invariance, which ensures that it respects Lorentz symmetry. In this formulation, the OSEFT Lagrangian looks formally equivalent to the sum over lightlike velocities of soft collinear effective field theory in the Abelian limit, but differences remain in the scale of the gauge fields involved in the two effective theories. We then use the OSEFT Lagrangian expanded in inverse powers of the on-shell energy to derive how the classical transport equations for charged massless fermions are corrected by quantum effects, as derived from quantum field theory. We provide a formulation in a full covariant way and explain how the consistent form of the chiral anomaly equation can be recovered from our results. We also show how the side-jump transformation of the distribution function associated with massless charged fermions can be derived from the reparametrization invariance transformation rules of the OSEFT quantum fields. Finally, we discuss the differences in our results with respect to others found in the literature.