Quark distribution functions in the chiral quark-soliton model: cancellation of quantum anomalies

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.