Higher order terms in the contraction of SO(3,2)

TL;DR

This paper investigates higher order terms arising from the contraction of the SO(3,2) group, revealing a connection between momentum spin contributions and electromagnetic interactions, including a derivation of the coupling constant.

Contribution

It introduces a detailed analysis of the momentum spin term in the contraction of SO(3,2), linking it to QED-like interactions and deriving the electromagnetic coupling constant.

Findings

Momentum spin contributes to multiparticle kinematics.

The interaction term resembles quantum electrodynamics.

The coupling constant matches Wyler's heuristic formula.

Abstract

The contraction of a spin-1/2 representation of the de Sitter group SO(3,2) yields a translation operator that consists of the usual momentum operator plus a second order term, the "momentum spin" as described by F. Guersey. The contribution of momentum spin to the kinematics of a multiparticle system in a tangential space of anti de Sitter space is analyzed. It is shown that it can be described by a perturbation term with the structure of the interaction term of quantum electrodynamics. An evaluation of the corresponding coupling constant reproduces Wyler's heuristic formula for the electromagnetic coupling constant.