Abstract
It is shown explicitly within the σ-model without nucleons and to any order in perturbation theory that the pion-vector current and the pion-axial vector current amplitudes satisfy the current algebra identity. The amplitude for pion production by an axial vector current satisfies a supplemented identity which includes terms arising from subtraction constants in the invariant amplitudes involved. The role of PCAC is investigated, and it is found that the generalized Ward identity is sufficient but not necessary for the current algebra identity to hold.
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