One massless particle equals two Dirac singletons

Abstract

The ‘remarkable representations of the 3+2 de Sitter group’, discovered by Dirac, later called singleton representations and here denoted Di and Rac, are shown to possess the following truly remarkable property: Each of the direct products Di ⊗ Di, Di ⊗ Rac, and Rac ⊗ Rac decomposes into a direct sum of unitary, irreducible representations, each of which admits an extension to a unitary, irreducible representation of the conformal group SO(4, 2). Therefore, in de Sitter space, every state of a free, ‘massless’ particle may be interpreted as a state of two free singletons — and vice versa. The term ‘massless’ is associated with a set of particle-like representations of SO(3, 2) that, besides the noted conformal extension, exhibit other phenomena typical of masslessness, especially gauge invariance.