Why Poincare symmetry is a good approximate symmetry in particle theory

TL;DR

This paper explores why Poincare symmetry is an effective approximate symmetry in particle physics by analyzing quantum representations of de Sitter and anti-de Sitter algebras, proposing a quantum-based explanation.

Contribution

It provides a quantum-level explanation for the approximate validity of Poincare symmetry using representation theory of anti-de Sitter algebra and solutions involving Dirac singletons.

Findings

Poincare symmetry emerges as an approximate symmetry when certain eigenvalues are large.

Explicit solutions with the required properties exist within the Dirac singleton framework.

The approach connects quantum representation theory with the classical limit of spacetime symmetries.

Abstract

As shown in the famous Dyson's paper "Missed Opportunities", even from purely mathematical considerations (without any physics) it follows that Poincare quantum symmetry is a special degenerate case of de Sitter quantum symmetries. Then the question arises why in particle physics Poincare symmetry works with a very high accuracy. The usual answer to this question is that a theory in de Sitter space becomes a theory in Minkowski space in the formal limit when the radius of de Sitter space tends to infinity. However, de Sitter and Minkowski spaces are purely classical concepts, and in quantum theory the answer to this question must be given only in terms of quantum concepts. At the quantum level, Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators $M_{4\mu}$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{\mu\nu}$ ($\mu,\nu=0,1,2,3$). We show that explicit solutions with such properties exist within the framework of the approach proposed by Flato and Fronsdal where particles that are considered elementary in the standard theory are bound states of two Dirac singletons.