BPHZL renormalization of 1/N expansion and critical behaviour of the three-dimensional chiral field

A modified soft mass renormalization scheme for 1/N expansion of the three dimensionalO(N)-invariant chiral field in the high- and low-temperature phases, as well as at the critical point, is constructed, free of infrared divergencies in each separate diagram. Generalized quantum chirality identities for composite operators are derived, from which the renormalizability of the model follows. The approach formulated here is applied to a rigorous analysis of the universal critical behaviour of theN-component chiral field in three dimensions.