On the quantisation of complex higher derivative theories and avoiding the Ostrogradsky ghost
On the quantisation of complex higher derivative theories and avoiding the Ostrogradsky ghost
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关于复杂高阶导数理论的量化和避免奥斯特罗格拉茨基幽灵
DOI：
10.1016/j.nuclphysb.2017.01.024
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
H. Veermae
中科院分区：
文献类型：
--
作者：
M. Raidal;H. Veermae
一般的高阶导数理论被认为从根本上是非物理的，因为它们包含奥斯特罗格拉茨基幽灵。我们表明，在复杂的经典力学是可能的，以构建更高的衍生理论，绕过Ostrogradsky定理，并有一个真实的能谱，是有界的从下面。复变理论可以正则量子化。由此产生的量子理论不受动力学不稳定性的影响，并且在不违反对应原理的情况下保持了通常的概率解释。作为概念证明，我们构造了一类稳定的相互作用复高阶导数理论，并给出了一个具体的例子。这个一致的和规范的框架使我们能够分析以前的尝试，以避免鬼使用非规范的量子化方案，如李-威克理论，狄拉克-泡利量子化或PT对称量子力学。理解任何动力学稳定的高阶导数理论中的幽灵的关键是接受它背后的复杂系统。
Generic higher derivative theories are believed to be fundamentally unphysical because they contain Ostrogradsky ghosts. We show that within complex classical mechanics it is possible to construct higher derivative theories that circumvent the Ostrogradsky theorem and have a real energy spectrum that is bounded from below. The complex theory can be canonically quantised. The resulting quantum theory does not suffer from the kinetic instability and maintains the usual probabilistic interpretation without violating the correspondence principle. As a proof of concept, we construct a class of stable interacting complex higher derivative theories and present a concrete example. This consistent and canonical framework allows us to analyse the previous attempts to avoid ghosts that use non-canonical quantisation schemes, such as the Lee–Wick theories, Dirac–Pauli quantisation orPT-symmetric quantum mechanics. The key to understand the would-be ghosts in any kinetically stable higher derivative theory is to accept the complex system behind it.