THE Q(2) EVOLUTION OF SOFFER INEQUALITY

DGLAP evolution equations may be presented in a form completely analog ous to the Boltzmann equation. This provides a natural proof of the po sitivity of the spin-dependent parton distributions, provided the init ial distributions at Q(0)(2) are also positive. in addition, the evolu tion to Q(2) < Q(0)(2) may violate positivity, providing therefore a ' time arrow'. The positivity condition is just \Delta P-ij(z)\less than or equal to P-ij(z) for z < 1 for all types of partons, while the '+' prescription and terms containing delta(1 - z) do not affect positivi ty. This method allows one to complete immediately the existing proof of Soffer inequality at leading and next-to-leading order. (C) 1998 El sevier Science B.V.