Hadron scattering amplitudes properties in the framework of axiomatic approach

Consequences of analyticity, unitarity and crossing symmetry for elementary particles scattering are considered at high, but finite energies. Classical results, which are valid at asymptotic energies, are reproduced by the corresponding passage to the limit. Different sum rules are considered, their equivalence to integral relations between real and imaginary parts of scattering amplitudes in question is shown. Connection between real and imaginary parts of symmetries as well as of antisymmetric scattering amplitudes, are considered uniformly. The dependence between the behavior of modulus and phase of scattering amplitude is investigated. It is shown, that approximation of dispersion relations by their local analogous is possible in case the scattering amplitude has no strong oscillations. Properties of oscillating amplitudes are analyzed. Upper bounds on total cross section and elastic scattering amplitude are considered. Absolute upper bounds for π0π0 elastic scattering, which are valid at arbitrary physical energies, are obtained