Lorentz group and mass spectrum of elementary particles

Abstract

Mass spectrum of localized states (elementary particles) of single quantum system is studied in the framework of Heisenberg's scheme. Localized states are understood as cyclic representations of a group of fundamental symmetry (Lorentz group) within a Gelfand-Neumark-Segal construction. It is shown that state masses of lepton (except the neutrino) and hadron sectors of matter spectrum are proportional to the rest mass of electron with an accuracy of $0,41\%$.