  In the framework of the chiral quark-soliton model of the nucleon we
investigate the properties of the polarized quark distribution. In particular
we analyse the so called anomalous difference between the representations of
the quark distribution functions in terms of occupied and non-occupied quark
states. By an explicit analytical calculation it is shown that this anomaly is
absent in the polarized isoscalar distribution \Delta u + \Delta d, which is
ultaviolet finite. In the case of the polarized isovector quark distribution
\Delta u - \Delta d the anomaly can be cancelled by a Pauli-Villars subtraction
which is also needed for the regularization of the ultraviolet divergence.

High Energy Physics - Phenomenology