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We formulate the on-shell effective field theory (OSEFT) in an arbitraryframe and study its reparametrization invariance (RI), which ensures that it isrespectful of Lorentz symmetry. In this formulation the OSEFT Lagrangian looksformally equivalent to the sum over light-like velocities of soft collineareffective field theory in the Abelian limit, differences remain in the scale ofthe gauge fields involved in the two effective theories. We then use the OSEFTLagrangian expanded in powers of the on-shell energy to derive how theclassical transport equations for charged massless fermions are corrected byquantum effects, as derived from quantum field theory. We provide a formulationin a full covariant way, and explain how the consistent form of the chiralanomaly equation can be recovered from our results. We also show how the sidejump transformation of the distribution function associated with masslesscharged fermions can be derived from the RI transformation rules of the OSEFTquantum fields. Finally, we discuss differences in our results with othersfound in the literature.

Consistent Relativistic Chiral Kinetic Theory: a derivation from OSEFT