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

TL;DR

The paper argues that the Standard Model's locality and ad hoc coupling constants can be reinterpreted as consequences of irreducible unitary representations of the Poincaré group, particularly through two-particle states. It shows that electromagnetic interactions and the fine-structure constant $\alpha$ arise from the normalization of two-particle Poincaré irreducible representations when the integration domain is a mass-shell subset $\Omega$ rather than the full $\mathbb{R}^4$, thereby regularizing perturbative integrals without breaking Poincaré invariance. Extending this to $N$ spinless particles leads to conformal gravity with a galaxy-specific constant $\kappa$ that matches observational estimates and can explain galactic dynamics without dark matter, suggesting Einstein gravity as a local limit. Overall, the framework links fundamental quantum structure to both particle interactions and cosmological gravity, offering a non-local, relativistic quantum-mechanical basis for the Standard Model and gravity. The discussion hinges on key relations such as $p^2 = M^2$, $p_1^2 = p_2^2 = m^2$, $W^{\mu\nu}$ in conformal gravity, and $\alpha = 4 \pi \omega^2$ derived from $\Omega$-domain normalization.

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.