Isometry generators in momentum representation of the Dirac theory on the de Sitter spacetime

Abstract

In this paper, it is shown that the covariant representation (CR) transforming the Dirac field under de Sitter isometries is equivalent to a direct sum of two unitary irreducible representations (UIRs) of the $Sp(2,2)$ group transforming alike the particle and antiparticle field operators in momentum representation. Their basis generators and Casimir operators are written down for the first time finding that these representations are equivalent to a UIR from the principal series whose canonical labels are determined by the fermion mass and spin. The properties of the conserved observables (i. e. one-particle operators) associated to the de Sitter isometries via Noether theorem and of the corresponding Pauli-Lubanski type operator are also pointed out.