论文标题
衍生类型的较高衍生理论的共鸣和稳定性
Resonance and stability of higher derivative theories of derived type
论文作者
论文摘要
我们考虑了高衍生场方程的类别，这些方程的波动算子是另一个较低顺序的另一个自动伴侣操作员的平方。在自由级别，该类别的模型被证明可以接受一系列两参数的运动积分。该系列包括规范能量。在这个系列中，每个保守数量都没有结合。相互作用包括在运动方程式中，以便在非线性级别保留数量序列中选定的代表。这些互动不一定是拉格朗日，但它们承认了哈密顿的动态形式。如果由于相互作用而从下方界定运动的积分，则该理论是稳定的。该动作在保守数量最小值的附近是有限的。波动的运动方程式具有衍生形式，没有共振。具有多频率和Podolsky电动力学的Pais-Uhlenbeck振荡器的模型来说明了一般构造。该示例也被认为是具有较高衍生物的稳定的非亚伯利亚阳米尔斯理论。
We consider the class of higher derivative field equations whose wave operator is a square of another self-adjoint operator of lower order. At the free level, the models of this class are shown to admit a two-parameter series of integrals of motion. The series includes the canonical energy. Every conserved quantity is unbounded in this series. The interactions are included into the equations of motion such that a selected representative in conserved quantity series is preserved at the non-linear level. The interactions are not necessarily Lagrangian, but they admit Hamiltonian form of dynamics. The theory is stable if the integral of motion is bounded from below due to the interaction. The motions are finite in the vicinity of the conserved quantity minimum. The equations of motion for fluctuations have the derived form with no resonance. The general constructions are exemplified by the models of the Pais-Uhlenbeck oscillator with multiple frequency and Podolsky electrodynamics. The example is also considered of stable non-abelian Yang-Mills theory with higher derivatives.
