Irreducible Multi-Particle Representations of the Poincar\'e Group as a Basis for the Standard Model

TL;DR

This paper explores the mathematical structure of multi-particle representations of the Poincaré group, linking them to electromagnetic and gravitational interactions, and suggests a non-local quantum mechanics framework that aligns with observed constants.

Contribution

It introduces a novel approach to particle interactions based on irreducible multi-particle Poincaré representations, providing a consistent non-local quantum mechanics perspective.

Findings

Electromagnetic coupling constant matches the normalisation factor of two-particle states.

A gravitational interaction derived from multi-particle representations matches experimental values.

Proposes a non-local, relativistic quantum mechanics framework for particle interactions.

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 Poincar\'e 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.