Pais-Ulhenbeck action的正则化及分支哈密顿问题的解决
Canonical formulation of Pais-Ulhenbeck action and resolving the issue of branched Hamiltonian
摘要：
在四阶Pais-Uhlenbeck振子作用量的上下文中Dirac的约束分析的缺点和广义四阶振子作用量的严重影响的相空间哈密顿量的出现，遵循Ostrogradski，Dirac和Horowitz的形式主义，需要一个可行的正则公式。这只有在端点处固定适当的变量并注意由变分原理得到的反曲面项之后才能实现。在这个过程中，不同高阶理论之间的一一对应关系已经建立。另一方面，拉格朗日函数中存在大于二次的速度时出现的分支汉密尔顿问题尚未得到唯一解决。然而，这些术语经常出现在高阶理论中，特别是引力。在这里，我们表明，规范制定的高阶理论需要照顾的问题优雅。
英文摘要：
Shortcomings of Dirac's constrained analysis in the context of fourth order Pais-Uhlenbeck oscillator action and the appearance of badly affected phase-space Hamiltonian for a generalized fourth order oscillator action, following Ostrogradski, Dirac and Horowitz's formalism, require a viable canonical formulation. This is achieved only after fixing appropriate variables at the end points and taking care of the counter surface terms obtained from variational principle. In the process a one-to-one correspondence between different higher order theories has been established. On the other hand the issue of branched Hamiltonian appearing in the presence of velocities with degree higher than two in the Lagrangian, has not been resolved uniquely as yet. However, often such terms appear with higher order theory, gravity in particular. Here we show that canonical formulation of higher order theory takes care of the issue elegantly.
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