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Explicit gauge covariant Euler—Lagrange equation

机译:显式量规协变量Euler-Lagrange方程

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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.
机译:在Euler-Lagrange方程中应用规范协变导数可以得到外力场的运动方程的捷径。标量协变导数包括外力作为导数的固有部分,因此简化了包含张量和标量协变场的拉格朗日数。协变量Euler-Lagrange方程中使用的规范协变量导数表示为张量分析中坐标协变量导数的扩展。几个例子提供了与广义相对论和规范理论研究有关的协变导数的有用证明。

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