We establish the direct $d=2$ on-shell bosonization $��_{L}(x_{+})=e^{i��(x_{+})}$ and $��_{R}^{\dagger}(x_{-})=e^{i��(x_{-})}$ in path integral formulation by deriving the off-shell relations $��_{L}(x)��_{R}^{\dagger}(x)=\exp[i��(x)]$ and $��_{R}(x)��_{L}^{\dagger}(x)=\exp[-i��(x)]$. Similarly, the on-shell bosonization of the bosonic commuting spinor, $��_{L}(x_{+})=ie^{-i��(x_{+})}\partial^{+}e^{-i��(x_{+})}$, $��^{\dagger}_{R}(x_{-})=e^{-i��(x_{-})-i��(x_{-})}$ and $��_{R}(x_{-})=ie^{i��(x_{-})}\partial^{-}e^{+i��(x_{-})}$, $��^{\dagger}_{L}(x_{+})=e^{i��(x_{+})+i��(x_{+})}$, is established in path integral formulation by deriving the off-shell relations $��_{L}(x)��^{\dagger}_{R}(x)=ie^{-i��(x)}\partial^{+}e^{-i��(x)}$ and $��_{R}(x)��^{\dagger}_{L}(x)=ie^{i��(x)}\partial^{-}e^{i��(x)}$.

18 pages, the final version to appear in Phys. Rev. D