带有约束的稳定高导数模型(英文)

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.

Stable higher derivative models with constraints by Hamiltonian analysis

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 in- volved 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 be- havior. 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.