# Massive poles in Lee-Wick quantum field theory

## TL;DR

This paper clarifies the pole structure in Lee-Wick quantum field theories, showing that only one physical pole exists near the real axis, with the others being artifacts or resonance structures, impacting how these theories are understood and calculated.

## Contribution

It reveals the true pole structure in Lee-Wick theories, correcting the common assumption of two complex conjugate poles and introducing a modified spectral representation.

## Key findings

- Only one physical pole near the real axis in Lee-Wick propagators
- Modified Lehmann representation includes resonance structures in spectral integrals
- Clarification of pole structures aids in better theoretical understanding

## Abstract

Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three pole-like structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral.