Quartic propagators, negative norms and the physical spectrum

Understand

Many arguments against quartic propagators, negative norm states and related effects concern the sicknesses which occur when the spectrum of the free particle Hamiltonian is formed.

• However, if the theory is more complicated, for example involving confinement such that the particle in question does not appear in the physical spectrum, those considerations do not apply directly.
• Path integral methods suggest that some of these may be acceptable theories.
• I provide an example that should be able to be simulated on a lattice which then allows a non-perturbative resolution of this question.