arXiv 2007.010632020-07hep-thgr-qc

Ostrogradsky定理的再思考：高阶导数拉格朗日量，鬼和退化

Reconsidering the Ostrogradsky theorem: Higher-derivatives Lagrangians, Ghosts and Degeneracy

Alexander Ganz, Karim Noui

备注：: 30 pages, 2 figures; few typos corrected

摘要：

我们审查的命运Ostrogradsky鬼高阶理论。我们首先回顾了原来的Ostrogradsky定理和说明，在经典力学的背景下，如何高导数拉格朗日导致无界哈密顿，然后导致（经典和量子）不稳定性。然后，我们将Ostrogradsky定理推广到几个动力学变量的高阶导数理论，并证明了在经典力学的背景下，当拉格朗日量“退化”时，避免Ostrogradsky不稳定性的可能性。特别是，我们解释了为什么高阶导数拉格朗日和/或高阶导数欧拉-拉格朗日方程不一定会导致传播的Ostrogradsky鬼。我们还研究了一些量子方面，并说明如何Ostrogradsky不稳定性出现在量子水平。最后，我们将我们的分析推广到高阶协变理论的情况下，由于哈密顿量是消失的，因此有界的，Ostrogradsky不稳定性的问题是微妙的。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文