守恒律与导出型场论的稳定性
Conservation Laws and Stability of Field Theories of Derived Type
摘要：
我们考虑的问题之间的对应关系的对称性和守恒量类的线性相对论性高导数理论的派生类型。在这类模型中，波算子是另一个形式上自伴算子的多项式，而时空的每一个等距都产生了作用泛函的一系列对称性。如果波算子由n阶多项式给出，那么这个级数包括n个独立的项，可以显式构造。然后利用Noether定理构造一个二阶守恒张量的n参数集。正则能量-动量张量包含在级数中，而其他项定义了独立的运动积分。拉格朗日锚的概念被应用到连接的一般保守张量的序列与原来的时空平移对称性。这一结果被解释为存在多个能量动量张量的类衍生系统。为了研究稳定性，我们寻求与时间平移有关的有界守恒量。我们观察到，导出的理论是稳定的，如果它的波算子是由一个多项式与简单的实根定义。一般的构造说明的例子的Pais-Uhlenbeck振荡器，高导数标量场，和扩展的陈-西蒙斯理论。
英文摘要：
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another formally self-adjoint operator, while each isometry of space-time gives rise to the series of symmetries of action functional. If the wave operator is given by n-th-order polynomial then this series includes n independent entries, which can be explicitly constructed. The Noether theorem is then used to construct an n-parameter set of second-rank conserved tensors. The canonical energy-momentum tensor is included in the series, while the other entries define independent integrals of motion. The Lagrange anchor concept is applied to connect the general conserved tensor in the series with the original space-time translation symmetry. This result is interpreted as existence of multiple energy-momentum tensors in the class of derived systems. To study stability we seek for bounded-conserved quantities that are connected with the time translations. We observe that the derived theory is stable if its wave operator is defined by a polynomial with simple and real roots. The general constructions are illustrated by the examples of the Pais-Uhlenbeck oscillator, higher-derivative scalar field, and extended Chern-Simons theory.
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