Sooner or later we must ask whether this law meets the test of relativistic invariance. 我们迟早要问:这个定律是否经得起相对论不变性的检验?
By introducing an infinitesimal generator for the relativistic Birkhoff system and based on the invariance of the differentiation variation principle under the infinitesimal transformations, the Noether theorem and Noether inverse theorem of the relativistic Birkhoff system are obtained. 定义相对论Birkhoff系统的无限小变换生成元,根据在无限小变换下微分变分原理的不变性,得到相对论Birkhoff系统的Noether定理和Noether逆定理。
Then the theory of Noether symmetries and Lie symmetries of the relativistic Birkhoff systems is obtained by the invariance of relativistic Pfaff action and relativistic Birkhoff equations under infinitesimal transformations. 根据在无限小变换下相对论Pfaff作用量的不变性和相对论Birkhoff方程的不变性,得到相对论Birkhoff系统的Noether对称性理论和Lie对称性理论;
The definition and criterion of Mei symmetry for the relativistic mechanical system are established, which are based upon the invariance of dynamical functions under infinitesimal transformations. 基于动力学函数在无限小变换下的不变性,建立了相对论性力学系统的Mei对称性的定义和判据;
A derivation of relativistic dynamics from the invariance of velocity interval directly 由速度间隔不变性直接推导相对论动力学