Irreducible Multi-Particle Representations of the Poincaré Group as a Basis for the Standard Model

Abstract

A phenomenological description of the Stern--Gerlach experiment yields a mathematical structure equivalent to that of a spin-1/2 particle, described by an irreducible unitary representation of the Poincaré group. In the corresponding irreducible two-particle representation, two-particle states have the form of an integral over product states. They describe a correlation between the particles with the structure of the electromagnetic interaction and a coupling constant that numerically equals the electromagnetic coupling constant. This coupling constant is essentially the normalisation factor of these two-particle states. The Standard Model of particle physics describes the electromagnetic interaction by a perturbation algorithm, where the experimental value of the electromagnetic coupling constant is inserted by hand. It is argued that it does not make sense to insert a normalisation factor without checking the range of integration of the corresponding integral and adjusting it if necessary. This adjustment provides the perturbation algorithm with the mathematically consistent structure of a non-local, relativistic, two-particle quantum mechanics. Similarly, multi-particle representations determine a gravitational interaction that, in the quasi-classical limit, is described by the field equations of conformal gravity. A calculated, galaxy-specific value of the gravitational constant matches the experimental value.