Dispersion Relations and Inconsistency of $\rho$ data
  The high energy elastic nucleon cross section is treated from the viewpoint of the basic principles of local field theory.   The connection between the energy dependence of $\sigma_{tot}$ and the $\rho$ - ratio of the real to imaginary parts of the forward elastic scattering amplitude is examined in the framework of dispersion relations, derivative dispersion relations and crossing symmetry. 
O.V. Selyugin