Partially conserved axial-vector current and model chiral field theories in nuclear physics

We comment on the relation between the two standard approaches to chiral symmetry-namely, the current algebra/partially conserved axial-vector current approach and the chiral Lagrangian method-in a manner intended to clarify recent and probable future applications of this symmetry in nuclear physics. Specifically, we show that in explicit chiral field theories the canonical $\pi N$ scattering amplitude does not have the famed "Adler zero" unless partial conservation of axial-vector current holds as an operator equation. This implies that there are a number of familiar chiral models in which the "Adler self-consistency" condition does not apply to the canonical pion field. Among the problems of current interest for which our remarks are relevant are the studies of the pion-nucleus optical potential, pion condensation, and the attempts to formulate a model field theory having both reasonable nuclear saturation and good low energy pion phenomenology.