Current commutation relations and pionic reactions

Abstract

The consequences imposed by the particular form of the equal-time commutators of current densities, which follows from the algebra of current operators, can be studied in two ways. It is possible to obtain first the consequences of the support conditions imposed on the equal-time commutator of two field theory operators, and then, to obtain the further relations imposed by the particular structure which appears in the algebraic relations. This is the approach followed here. In so doing, particular attention is paid to nearby singularities and the only assumption made is that, once the contribution of these terms has been obtained, the remainder is a slowly varying function. The other, and currently used, approach consists in obtaining directly relations, which already include the strong constraints imposed by the algebraic relations, notwithstanding the more general and weaker constraints imposed on the Fourier transform of an equal-time commutator of two field operators. These more general and weaker constraints alone yield, in particular, the consistency relations imposed by the PDDAC (pion dominance of the divergence of the axial current) hypothesis. Several relations for pionic reactions are presented.