Spinning fields on Sd and dSd , unitary irreducible representations, and ladder operators

Abstract

We construct, for spin 0,1,2 tensor fields on Sd, a set of ladder operators that connect the distinct unitary irreducible representations (UIRs) of SO(d+1). This is achieved by relying on the conformal Killing vectors of Sd. For the case of spinning fields, the ladder operators generalize previous expressions with a compensating transformation necessary to preserve the transversality condition. We then extend the results to the exceptional/discrete UIRs of SO(d,1), again relying on the conformal Killing vectors of de Sitter space. Our construction recovers the conventional conformal primary transformations for the scalar fields when the mass term leads to conformal coupling. A similar approach for the spin-2 field leads to the conformal-like operators found recently. Published by the American Physical Society 2025