Spin-dependent conformally invariant integral transform

Abstract

As an extension of the Hilbert transform, which characterizes the spacetime conformally invariant integral transform, we show that, based on the Bhabha theory, a spin-dependent conformally invariant integral transform can be written as a product of the spin-independent integral transform and the Casimir operator of the corresponding conformal group. In contrast to an ordinary context, where spacetime translation symmetry is assumed, we introduce an intrinsic momentum operator, by which the Casimir operator turns out to be spacetime dependent (spin-orbit coupling, Pauli-Lubanski pseudo vector, and the like). We also show that the physical state annihilated by the intrinsic momentum operator represents a spin-s state.