Bound States in Lee's Complex Ghost Model

TL;DR

This paper investigates bound states in Lee's complex ghost model within quantum field theories with higher derivatives, revealing that unitarity violation is linked to the non-existence of bound states and complex delta functions.

Contribution

It demonstrates that bound states cannot be formed from ghosts via complex delta functions, providing insight into unitarity issues in Lee-Wick type models.

Findings

Bound states are not generated by ghosts through complex delta functions.

Unitarity violation is associated with the non-existence of bound states.

The complex delta function differs from the Dirac delta, affecting unitarity.

Abstract

Quantum field theories (QFTs) including fourth-derivative terms such as the Lee-Wick finite QED and quadratic gravity have a better ultra-violet behavior compared to standard theories with second-derivative ones, but the existence of ghost with negative norm endangers unitarity. Such a ghost in general acquires a pair of complex conjugate masses from radiative corrections whose features are concisely described by the so-called Lee model. Working with the canonical operator formalism of QFTs, we investigate the issue of bound states in the Lee model. We find that the bound states cannot be created from ghosts by contributions of a complex delta function, which is a complex generalization of the well-known Dirac delta function. Since the cause of unitarity violation in the Lee-Wick model is the existence of the complex delta function instead of the Dirac delta function, it is of interest to notice that the violation of the unitarity is also connected to the non-existence of bound states. Finally, the problem of amelioration of the unitarity in quadratic gravity is briefly discussed.