Derivative Dispersion Relations

We discuss some analytical and numerical aspects related to the replacement of integral dispersion relations by derivative relations and also the practical applicability of the derivative approach in the investigation of high-energy elastic hadron-hadron scattering. Making use of a Monopole Pomeron model and singly subtracted integral and derivative dispersion relations, we present the results of fits to the experimental data on the total cross sections and the ratio of the real to the imaginary part of the forward elastic scattering amplitude (proton-proton and antiproton-proton interactions). The emphasis is on the region of low energies and, in particular, we show that once the subtraction constant is used as a free fit parameter the derivative approach is equivalent to the integral approach even below the energy cutoff of the fitted data.