On some consequences of the Snyder-Sidharth deformation of Special Relativity

The hypothesis on a minimal scale existence in the Universe leads to noncommutative geometry of Spacetime and thence to a modification of the Special Relativity constraint. Sidharth has deduced that this is equivalent to the Lorentz symmetry violation. This latter consideration was also used by Glashow, Coleman and other scholars though based on purely phenomenological models that have been suggested by the observation of Ultra High Energy Cosmic Rays and Gamma Bursts. On the other hand a parallel development has been the proposal of a small but nonzero photon mass $m_\gamma>0$ by some authors including Sidharth, such a mass being within experimentally allowable limits. This too leads to a small violation of the Lorentz symmetry observable in principle in very high energy gamma rays, as in fact is claimed. In this paper we study the Snyder--Sidharth Hamiltonian and briefly comment the Dirac--Sidharth Hamiltonian, that is a possible explanation for observable violation of the Lorentz symmetry.