Dispersion relations for pion nucleon scattering in the framework of localizable field theories

Unidimensional dispersion relations in terms of the field localizable theories are presented for the pion-nucleon scattering amplitude according to the energy variable E at a fixed value of momentum transfer p2 from the interval 0(<=)p2(<=) 32/3x2M+m/2M-mxm2, when mathematical expectations of physical operators in a pulse space beyond the mass surface admit the growth not stronger than the arbitrary linear exponent and in the configuration space do not satisfy ordinary properties of locality. Analytical properties of the scattering amplitude necessary to prove such dispersion relations are studied by means of the Jost-Lehmann-Dyson integral representation proved in terms of the field localizable theories