Acausality and dispersion relations

This paper is concerned with the study of the analytic properties of the scattering amplitude under the assumption that the signal propagates not only inside the light cone but also outside it, however near its surface or its vertex. The conditions of macroscopic causality and spectrality were fulfilled. It is shown that the dispersion relations are violated throughout the energy region. Therefore, a check of these dispersion relations may be of principal importance for the theory.