Physical interpretation of complex-energy negative-metric theories

Abstract

It has long been held that the divergences of field theory could be removed if the theory was formulated on a Hilbert space with an indefinite metric. The difficulty of this approach was that the theory then possessed channels with negative probability and therefore violated unitarity. In a recent paper, Lee and Wick have observed that this difficulty could be eliminated if negative-metric states had complex energy. In this paper, we produce a model which shows several of the difficulties associated with the Lee-Wick proposal. The existence of complex energies leads to interpretation difficulties and, in higher sectors, does not completely solve the unitarity problem. We use the model to show how the Lee-Wick conjecture can be extended to overcome the difficulties that are produced. We describe the physical meaning of "good" theories with an indefinite metric.