New derivation of the Altarelli-Parisi equations

The Altarelli-Parisi equations are derived without using (1-z${)}_{+}$ regularization and δ(1-z) function insertion. We find that virtual diagrams from renormalization give a negative contribution to parton evolution and the effect of these virtual diagrams is equivalent to that of some real diagrams with opposite sign. In this new approach, momentum conservation and valence-quark-number conservation of parton-number densities are satisfied automatically. A consistent probabilistic picture of parton evolution inside a hadron is also given.