Iterated Kleinian equations

Abstract

A higher order field has different forms of excitation. Some of them have negative energies. The signs of the quantization rules depend on the signs of the energies. An abnormal sign implies a negative sign of the residue at the on-shell pole of the propagator, leading to a clash with unitarity. To change these signs we can change the identification of the creation and annihilation operators. But then the energy has no lower bound. The way out is found by adopting a symmetric vacuum state. The corresponding propagator is a half retarded and half advanced Green function. It has a zero residue at the on-shell pole. There is no associated free particle. The abnormal modes act only as mediators of interactions.