| 摘要: |
| 给出了一类精确可解的高导数模型,表明了约束如何去除高导数带来的Ostrogradski不稳定性,对于作用量含有二阶时间导数的系统,找到了建立稳定约束系统的充分必要条件. |
| 关键词: Pais-Uhlenbeck振子 Ostrogradski不稳定性 高导数模型 约束系统 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Stable higher derivative models with constraints by Hamiltonian analysis |
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ZHAI Xianghua, AO Xichen
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Shanghai United Center for Astrophysics (SUCA), Shanghai Normal University
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| Abstract: |
| In this paper,we present a class of exactly solvable higher derivative models with and without constraints based on the Pais-Uhlenbeck Oscillator,through which we show explicitly how the constraints remove the Ostrogradski instability brought by higher derivatives.We find the sufficient and necessary condition to establish a stable system with constraints,in which the Lagrangian is involved with 2nd time derivative.We also generalize the investigations of linear systems to a higher derivative system with an arbitrary potential term.We propose a criterion of choosing constraints,which is to eliminate the harmful and retain the favorable in physics from the original dynamic behavior.In the linear case,this criterion would enable us to eliminate the unstable QNMs and retain the stable ones.All these discussions would help us to find a reasonable field theory with higher derivatives. |
| Key words: Pais-Uhlenbeck Oscillator Ostrogradski instability higher derivative models constraints |
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