Equal-time current commutator and sum rules in axiomatic field theory

On the basis of Vladimirov's theorems [1] a study is made of the equal-time current commutator in axiomatic quantum field theory. It is shown how the structure and the number of Schwinger terms depend on the asymptotic behavior at infinity of the Fourier transforms of the retarded functions. This makes it possible to formulate conditions sufficient for the derivation of Gell-Mann–Fubini sum rules.