Abstract
The convolution theorem is used to obtain general sum rules for the Khuri amplitudes of the current correlation function (familiar from current algebra). The sum rules can be continued analytically in the Khuri λ-plane to negative integer values of λ; at these points the sum rules relate the finite-energy integral to the Fourier transform of distributions that, by the Gel'fand-Shilov method of analytic continuation, can be defined in a natural way as the current commutator and its derivatives on the light-cone. Assuming that the current commutator involved has a light-cone Wilson expansion, one can write the previously mentioned sum rules in terms of scaling amplitudes. Finally one considers the peculiar features of the sum rules obtained in the case of conserved currents.
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