Remarks on ghost resonances

TL;DR

This paper investigates the mathematical structure and physical implications of ghost resonances in quantum field theory, focusing on pole locations, analytic continuations, and the necessity of finite-time formulations.

Contribution

It provides a detailed analysis of ghost propagators, highlighting their unique pole structure and emphasizing the importance of finite-time quantum field theories for consistent descriptions.

Findings

Ghost propagator has complex conjugate poles in the first sheet for real masses above threshold.

Different prescriptions (Feynman, anti-Feynman, fakeon) are analyzed for defining ghost propagators.

Finite-time quantum field theories are essential for accurately capturing ghost resonance properties.

Abstract

In this paper we study various aspects of ghost resonances: the resummation that leads to the dressed propagator, the poles locations, the analytic continuation into the second Riemann sheet and the spectral representations in both first and second sheets. In particular, we show that for real masses above the multiparticle threshold the ghost propagator has a pair of complex conjugate poles in the first sheet, unlike the case of an ordinary unstable resonance which has no pole in the first sheet but a complex conjugate pair in the second sheet. Mathematical and physical implications of this feature are discussed. We also clarify an important point regarding the two absorptive contributions of a ghost propagator in the narrow-width approximation. Furthermore, we argue that finite-time quantum field theories are needed to consistently derive the dressed ghost propagator and capture the true physical properties of ghost resonances. Throughout the work, different prescriptions to define the ghost propagator on the real axis are considered: Feynman, anti-Feynman and fakeon prescriptions.