Consistency Conditions on the Strong Interactions Implied by a Partially Conserved Axial-Vector Current. II

Consequences of the partially conserved axial-vector current (PCAC) hypothesis are explored. A set of simple rules is derived which relate the matrix element for any strong interaction process with the matrix element for the corresponding process in which an additional zero-mass, zero-energy pion is emitted or absorbed. A generalization to include lowest order electromagnetic processes is given. A theorem is stated and proved which shows how divergence equations of the form ${\ensuremath{\partial}}_{\ensuremath{\lambda}}{J}_{\ensuremath{\lambda}}=D$ are modified when a minimal electromagnetic interaction is switched on.