Using Fundamental Physical Constants to Determine the Properties of Quantum Particles

Abstract

The general Lie algebra for quantum operators of coordinates, momentum, and angular momentum of a quantum particle is investigated. In the limiting case, it becomes a Lie algebra for operators of canonical quantum field theory. Relations between operators of space-time symmetries of a quantum particle are considered. Operators obey a generalized algebra that depends on three new fundamental constants with dimensions of mass M, length L, and action H. Using representations of this algebra, we form generalized quantum HLM-fields with which HLM quantum particles are associated. It is shown that to take into account specific properties of these particles, it is necessary to modify the procedure of quantum measurements.