论文标题
具有高阶时间衍生物和Ostrogradsky Ghost的理论
Theories with higher-order time derivatives and the Ostrogradsky ghost
论文作者
论文摘要
Newtons第二定律，Schrodingers方程和Maxwells方程都是由最多的第二次衍生物组成的理论。确实，我们不经常需要花时间派生的加速度。那么，为什么我们看不到更多高阶衍生理论呢？尽管一些研究表现出较高的衍生物在二次重力和标量场理论中的实用性，但最终将遇到问题。 1850年，物理学家Mikhail Ostrogradsky提出了一个定理，该定理指出，由有限的高阶高阶时间衍生物组成的非排分拉格朗日式导致汉密尔顿人从下面没有结合。明确地表明，这种系统的哈密顿量包括物理动量中的线性，通常称为Ostrogradsky Ghost。本论文研究如何通过考虑堕落的拉格朗日人对这一动量施加约束来避免Ostrogradsky鬼魂。该研究首先显示了幽灵的存在，后来涵盖了对二阶时间派生系统进行的汉密尔顿约束分析所需的基本形式主义，这些系统都是单变量和系统耦合到常规的系统。最终，堕落的二阶拉格朗日人通过产生二级约束来限制物理动量，成功地消除了Ostrogradsky Ghost。此外，最后提出了对一般高级拉格朗日的哈密顿分析的概述。
Newtons second law, Schrodingers equation and Maxwells equations are all theories composed of at most second-time derivatives. Indeed, it is not often we need to take the time derivative of the acceleration. So why are we not seeing more higher-order derivative theories? Although several studies present higher derivatives usefulness in quadratic gravity and scalar-field theories, one will eventually encounter a problem. In 1850, the physicist Mikhail Ostrogradsky presented a theorem that stated that a non-degenerate Lagrangian composed of finite higher-order time derivatives results in a Hamiltonian unbounded from below. Explicitly, it was shown that the Hamiltonian of such a system includes linearity in physical momenta, often referred to as the Ostrogradsky ghost. This thesis studies how one can avoid the Ostrogradsky ghost by considering degenerate Lagrangians to put constraints on the momenta. The study begins by showing the existence of the ghost and later cover the essential Hamiltonian formalism needed to conduct Hamiltonian constraint analyses of second-order time derivative systems, both single-variable and systems coupled to a regular one. Ultimately, the degenerate second-order Lagrangians successfully eliminate the Ostrogradsky ghost by generating secondary constraints restricting the physical momenta. Moreover, an outline of a Hamiltonian analysis of a general higher-order Lagrangian is presented at the end.
