Abstract
We examine the Weinberg sum rules in a perturbation theoretic calculation based on the σ-model and find that only the first sum rule is valid. The same is true in a low-order quark-model calculation. A number of constraints on the invariant amplitudes for the three-point function are found to be inconsistent with the perturbation-theory calculation unless we permit either a covariant Schwinger term in the equal-time commutator or include seagull graphs in our model, thus demonstrating their equivalence.
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