Prototype models for particle structure in gauge supersymmetry

Particle content in prototype models of gauge supersymmetry is examined. The properties of the prototype models which are in common with those of gauge supersymmetries are the initial non-diagonality of the quadratic part of the action, global supersymmetry invariance and the existence of a mass parameter in the quadratic part of the action. The analysis exhibits the particle content of prototype models to consist of normal poles and sets of complex conjugate poles on the physical sheet. Diagonalization of the hamiltonian can be carried out for such systems (in contrast to the prototype model of conformal supergravity where dipole ghosts arose). Essentially the pole structure observed in the prototype models of gauge supersymmetry is the supersymmetric analogue of the Lee-Wick phenomenon where the normal and the complex conjugate poles form global multiplets.