Anti-Instability of Complex Ghost

Abstract

We argue that Lee-Wick's complex ghost appearing in any higher derivative theory is stable and its asymptotic field exists. It may be more appropriate to call it ``anti-unstable" in the sense that, the more the ghost `decays' into lighter ordinary particles, the larger the probability the ghost remains as itself becomes. This is explicitly shown by analyzing the two-point functions of the ghost Heisenberg field which is obtained as an exact result in the $N\rightarrow\infty$ limit in a massive scalar ghost theory with light $O(N)$-vector scalar matter. The anti-instability is a consequence of the fact that the poles of the complex ghost propagator are located on the physical sheet in the complex plane of four-momentum squared. This should be contrasted to the case of the ordinary unstable particle, whose propagator has no pole on the physical sheet.