Altarelli-Parisi Equation in Non-Equilibrium QCD

The $Q^2$ evolution of fragmentation function in non-equilibrium QCD by using DGLAP evolution equation may be necessary to study hadron formation from quark-gluon plasma at RHIC and LHC. In this paper we study splitting functions in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. For quarks and gluons with arbitrary non-equilibrium distribution functions $f_q(\vec{p})$ and $f_g(\vec{p})$, we derive expressions for quark and gluon splitting functions in non-equilibrium QCD at leading order in ${\alpha }_s$. We make a comparison of these splitting functions with that obtained by Altarelli and Parisi in vacuum.