标题： (1+1)维经典场论中的幽灵相互作用 显示英文标题

标题： Ghostly interactions in (1+1) dimensional classical field theory

摘要： 我们研究了在1+1维闵可夫斯基时空中的两个耦合标量场的古典稳定性，这些场具有相反符号的动能项。 在第一部分中，我们描述了未被抑制的鬼魅相互作用，并提供了支持以下陈述的数值解。 首先，古典不稳定性不是瞬时的，甚至可能是良性的，即没有有限时间奇点。 其次，虽然古典不稳定性可以向更高频率的激发状态传播，但它并非由高频模式驱动： 在固定振幅下，高频模式比低频模式更稳定。 在第二部分中，我们证明了质量项可以抑制古典不稳定性。 特别是，我们举例说明，高频率的鬼魅场似乎不会违反解耦定理，并且可以经典地被积分掉。 在第三部分中，我们展示了自相互作用如何抑制不稳定性，例如通过将不稳定性发生的时间推迟到参数上很大的时间。 将大但有限演化时间的数值结果外推到无限演化时间，我们证明了围绕平凡和非平凡场论真空的古典涨落随着（i）涨落的初始振幅更小，（ii）涨落的初始频率更高，（iii）场的质量更大，或（iv）相互作用耦合更弱而变得越来越持久。 此外，我们对一些全局稳定的鬼魅力学模型的场论推广进行的数值模拟并未表现出任何不稳定性。 显示英文摘要

摘要： We investigate the classical stability of two coupled scalar fields with opposite-sign kinetic terms evolving in 1+1 dimensional Minkowski spacetime. In the first part, we characterise unquenched ghostly interactions and present numerical solutions that support the following statements. First, the classical instability is not instantaneous and can even be benign, i.e., free of finite-time singularities. Second, while the classical instability can cascade towards higher frequency excitations, it is not driven by high frequency modes: At fixed amplitude, high-frequency modes are more stable than low-frequency modes. In the second part, we demonstrate that the classical instability can be quenched by mass terms. In particular, we exemplify that heavy high-frequency ghost fields seem to not violate the decoupling theorem and can be integrated out classically. In the third part, we demonstrate how self-interactions can quench the instability, for instance, by postponing its onset to parametrically large times. Extrapolating numerical results at large but finite evolution time to infinite evolution time, we demonstrate that classical fluctuations around trivial and nontrivial field-theory vacua are increasingly long-lived with (i) smaller initial amplitude of fluctuations, (ii) higher initial frequency of fluctuations, (iii) larger masses of the fields, or (iv) weaker interaction coupling. Moreover, our numerical simulations for field-theoretical generalisations of some globally-stable ghostly mechanical models do not feature any instability.