  We discuss a novel world-line framework for computations of the Chiral
Magnetic Effect (CME) in ultrarelativistic heavy-ion collisions. Starting from
the fermion determinant in the QCD effective action, we show explicitly how its
real part can be expressed as a supersymmetric world-line action of spinning,
colored, Grassmanian particles in background fields. Restricting ourselves for
simplicity to spinning particles, we demonstrate how their constrained
Hamiltonian dynamics arises for both massless and massive particles. In a
semi-classical limit, this gives rise to the covariant generalization of the
Bargmann-Michel-Telegdi equation; the derivation of the corresponding Wong
equations for colored particles is straightforward. In a previous letter we
outlined how Berry's phase arises in a non-relativistic adiabatic limit for
massive particles. We extend the discussion here to systems with a finite
chemical potential. We discuss a path integral formulation of the relative
phase in the fermion determinant that places it on the same footing as the real
part. We construct the corresponding anomalous world-line axial vector current
and show in detail how the chiral anomaly appears. Our work provides a
systematic framework for a relativistic kinetic theory of chiral fermions in
the fluctuating topological backgrounds that generate the CME in a deconfined
quark-gluon plasma. We outline some further applications of this framework in
many-body systems.
