Numerical Investigations of Stable Dynamics in the Presence of Ghosts

TL;DR

This study investigates the nonlinear dynamics of classical field theories with ghost degrees of freedom, revealing conditions under which such systems can exhibit long-lived, metastable behavior instead of immediate instability.

Contribution

The paper provides a systematic numerical analysis showing how spectral content, amplitude, and nonlinear interactions influence the stability and metastability of ghost-containing classical field theories.

Findings

Ghost-normal systems can have long-lived bounded evolution.

Ultraviolet-dominated and small-amplitude configurations are more stable.

Certain nonlinear potentials can generate metastable regimes that suppress ghost growth.

Abstract

We explore the nonlinear dynamics of classical field theories containing ghost degrees of freedom, focusing on two coupled scalar fields with opposite kinetic terms in (1+1) and (2+1) dimensional Minkowski spacetime. Using a spacetime finite element formulation, we perform a systematic numerical study across a broad class of initial data. We find that ghost-normal systems can exhibit long-lived, dynamically bounded evolution over extended time intervals, with stability strongly controlled by spectral content and amplitude. Ultraviolet-dominated and small-amplitude configurations remain stable significantly longer than infrared-dominated or large-amplitude data, indicating that instability is mediated by nonlinear spectral energy transfer rather than instantaneous runaway. Nonlinear self-interactions play a dual role: while they can accelerate energy exchange between sectors, certain potentials, including a lifted $\phi^6$ interaction supporting oscillon-like structures, generate transient metastable regimes that partially suppress ghost-induced growth. Our results demonstrate that the dynamical consequences of ghost modes in classical field theory depend sensitively on dispersion, nonlinearity, and phase structure, revealing a richer metastability landscape than commonly assumed.