New Quantum Mechanics –A Trial beyond Special Relativity–

Abstract

The new version of quantum mechanics (QM) with the finite momentum space (maximum momentum value K ) is presented along the line already described in the series of papers by the present author. Our QM is a generalized version of the relativistic QM proposing generalized Lorentz transformations forming a non-abelian group, a specific and convenient form of the set of transformations among “general relativistic transformations”. Our theory offers an intermediate type of “relativity” between special relativity (SR) and general relativity (GR). One of interesting consequences is described for the neutrino flux from very high energy particle–particle (say hadron–hadron or lepton–hadron) collisions, which gives the ratio of neutrino mass m ν and the maximum momentum K . Bound states should have the maximum momenta ν K , with ν being a positive integer and fractional number. Also quantum field theories are briefly mentioned.