Fundamental role of Dirac supersingletons in particle theory

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 goes 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 M4a of the anti-de Sitter algebra are much greater than the eigenvalues of the representation operator Mab (a, b=0,1,2,3). We show that an explicit solution with such properties exists within the framework of the approach proposed by Flato and Fronsdal where standard elementary particles are bound states of two Dirac singletons.