Consistent Relativistic Chiral Kinetic Theory: a derivation from OSEFT

TL;DR

This paper develops a Lorentz-invariant on-shell effective field theory for massless fermions, deriving quantum-corrected transport equations and clarifying the chiral anomaly and side jump phenomena.

Contribution

It formulates a reparametrization-invariant OSEFT framework, deriving quantum corrections to classical transport equations and elucidating the chiral anomaly and side jump effects.

Findings

Derived covariant quantum-corrected transport equations.

Reproduced the consistent form of the chiral anomaly.

Explained the origin of side jump transformations.

Abstract

We formulate the on-shell effective field theory (OSEFT) in an arbitrary frame and study its reparametrization invariance (RI), which ensures that it is respectful of Lorentz symmetry. In this formulation the OSEFT Lagrangian looks formally equivalent to the sum over light-like velocities of soft collinear effective field theory in the Abelian limit, differences remain in the scale of the gauge fields involved in the two effective theories. We then use the OSEFT Lagrangian expanded in 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 RI transformation rules of the OSEFT quantum fields. Finally, we discuss differences in our results with others found in the literature.