Group Theory and Mass Quantization

Abstract

The mass spectrum problem (the 14th Ginzburg's problem) is analyzed in terms of the conventional reductional and alternative holistic frameworks. From the holistic viewpoint, substance (the same as energy) is the primary concept and particles are secondary and emergent. An axiomatic system is proposed where the basic notion of the spectrum of matter is defined, and the particle spectrum emerges as a result of the energy/mass quantization. A new mass formula is derived in terms of the quantum numbers related to the Lorentz group Casimir eigenvalues. It is shown that the masses of states in the lepton and hadron sectors of the spectrum of matter are proportional to the electron rest mass (quantum of mass) with an accuracy of $0,41\%$ on average.