  Theoretical understanding of the observed jet quenching measurements at RHIC
and LHC is challenging in QCD because it requires understanding of parton to
hadron fragmentation function in non-equilibrium QCD. In this paper, by using
closed-time path integral formalism, we derive the gauge invariant definition
of the gluon to hadron fragmentation function in non-equilibrium QCD which is
consistent with factorization theorem in non-equilibrium QCD from first
principles.
