2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190656Explicit exact formulas are presented, for the leading order term in a strict chiral covariant derivative expansion, for the abnormal parity component of the effective action of two- and four-dimensional Dirac fermions in presence of scalar, pseudo-scalar, vector and axial vector background fields. The formulas hold for completely general internal symmetry groups and general configurations. In particular the scalar and pseudo-scalar fields need not be on the chiral circle.45 pages, REVTEX, no figures. Minor correctionsHigh Energy Physics - Theorytext