General invertible transformation and physical degrees of freedom
General invertible transformation and physical degrees of freedom
复制标题
DOI：
10.1103/physrevd.95.084053
复制
发表时间：
2017-02
影响因子：
5
通讯作者：
Kazufumi Takahashi;H. Motohashi;T. Suyama;Tsutomu Kobayashi
中科院分区：
文献类型：
--
作者：
Kazufumi Takahashi;H. Motohashi;T. Suyama;Tsutomu Kobayashi
可逆域变换是旧域变量与新域变量一一对应的变换。因此，人们可能认为通过可逆变换相关的两个系统在物理上是等价的。然而，如果变换依赖于场的导数，则由于运动方程中出现了高阶导数项，两个系统之间的等价性是不平凡的。为了解决这个问题，我们证明了以下关于可逆变换和欧拉-拉格朗日方程之间关系的定理：如果场变换是可逆的，则原始欧拉-拉格朗日方程组的任何解都映射到新欧拉-拉格朗日方程组的解，反之亦然。我们还提出了应用程序的定理标量张量理论。
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.