Spin degrees of freedom incorporated in conformal group: Introduction of an intrinsic momentum operator

Abstract

Considering spin degrees of freedom incorporated in the conformal generators, we introduce an intrinsic momentum operator \pi_\muπμ, which is feasible for the Bhabha wave equation. If a physical state \psi_{ph}ψph for spin s is annihilated by the \pi_\muπμ, the degree of \psi_{ph}ψph, deg \psi_{ph}ψph, should equal twice the spin degrees of freedom, 2 ( 2 s + 1)2(2s+1) for a massive particle, where the multiplicity 22 indicates the chirality. The relation deg \psi_{ph}ψph = 2(2s+1) holds in the representation R_5R5 (s,s), irreducible representation of the Lorentz group in five dimensions.