  In this paper we prove factorization of fragmentation function in
non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral
formalism. We use the background field method of QCD in a pure gauge in path
integral approach to prove factorization of fragmentation function in
non-equilibrium QCD. Our proof is valid in any arbitrary gauge fixing parameter
$\alpha$. This may be relevant to study hadron production from quark-gluon
plasma at high energy heavy-ion colliders at RHIC and LHC.
