显式规范协变欧拉-拉格朗日方程
Explicit gauge covariant Euler-Lagrange equation
摘要：
将规范协变导数应用于欧拉-拉格朗日方程，得到了求解受外力作用场的运动方程的捷径。规范协变导数包含一个外力作为导数的固有部分，因此简化了包含张量和规范协变场的拉格朗日量。作为张量分析中坐标协变导数的推广，给出了协变欧拉-拉格朗日方程中的规范协变导数。几个例子提供了有用的示范相关的研究在广义相对论和规范理论的协变导数。
英文摘要：
The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic part of the derivative and hence simplifies Lagrangians containing tensor and gauge covariant fields. The gauge covariant derivative used in the covariant Euler-Lagrange equation is presented as an extension of the coordinate covariant derivative used in tensor analysis. Several examples provide useful demonstrations of the covariant derivative relevant to studies in general relativity and gauge theory.
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