Nonrelativistic Elementary Particles

Yuri A. Rylov

One uses the investigation strategy: ”Find a mistake in foundation of physics and correct it”. Two fundamental defects are corrected: (1) nonrelativistic concept of the particle state, (2) inadequacy of the differential geometry formalism at the metric approach to geometry. Usage of relativistic concept of the particle state admits one to create united formalism for description of deterministic and stochastic particles motion. The quantum mechanics is founded as a statistical description of the stochastic particles motion. Stochasticity of the quantum particles motion is explained by multivariance of the space-time geometry, which leads to the world lines wobbling of elementary particles. Relativistic concept of the particle state and the metric approach to the space-time geometry admit one to construct the skeleton conception of elementary particles. The skeleton conception admits one to investigate the arrangement of elementary particles (but not only to systamatize them, ascribing quantum numbers to them).

Wesley E. Brittin, A.Y. Sakakura

A new fundamental theory of composite particles in nonrelativistic many-body systems is developed. The theory is constructed making use solely of the physical Fock space for the basic elementary particles which comprise the many-body system. In this manner exchange symmetry in the elementary particles is exact. Physical composite particle creation and annihilation operators are introduced and these operators satisfy exact Bose (Fermi) commutation (anticommutati$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{o}}$n) relations depending on whether the composites correspond to bosons or to fermions. Commuting physical occupation number operators for composite particles are then constructed in the usual manner from the composite creation and annihilation operators. These number operators are highly dressed in terms of the basic elementary particle operators. Finally, the foundations of statistical mechanics for bound composite particles are formulated in terms of the appropriate occupation number operators.

N. Giovannini

We apply a recently developed mathematical formalism to the kinematical classification of elementary physical systems, more precisely to the derivation of the possible state spaces for single (massive) particles and to their corresponding group theoretical interpretation. We show in particular that in all considered cases, relativistic or not, we find in a unified way two solutions, a quantal one and a classical one.