论文标题
重新考虑Ostrogradsky定理：高衍生物拉格朗日，鬼与堕落
Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy
论文作者
论文摘要
我们在高阶理论中回顾了Ostrogradsky Ghost的命运。我们首先回忆起原始的Ostrogradsky定理，并在古典力学的背景下说明了更高衍生品的Lagrangians如何导致无限的汉密尔顿人，然后导致（古典和量子）的不稳定性。然后，我们将Ostrogradsky定理扩展到几个动力学变量的高源理论，并显示出在拉格朗日“退化”时逃避Ostrogradsky不稳定性的可能性，但仍在古典力学的背景下。特别是，我们解释了为什么更高衍生的Lagrangians和/或更高衍生品Euler-Lagrange方程不一定会导致Ostrogradsky Ghost的传播。我们还研究了一些量子方面，并说明了Ostrogradsky不稳定性如何在量子水平上显示出来。最后，我们将分析概括为高阶协变量理论的情况，随着哈密顿量消失并因此有限，Ostrogradsky不稳定性的问题是微妙的。
We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables and show the possibility to evade the Ostrogradsky instability when the Lagrangian is "degenerate", still in the context of classical mechanics. In particular, we explain why higher-derivatives Lagrangians and/or higher-derivatives Euler-Lagrange equations do not necessarily lead to the propagation of an Ostrogradsky ghost. We also study some quantum aspects and illustrate how the Ostrogradsky instability shows up at the quantum level. Finally, we generalize our analysis to the case of higher order covariant theories where, as the Hamiltonian is vanishing and thus bounded, the question of Ostrogradsky instabilities is subtler.
