论文标题
揭开针对现场理论的拉格朗日形式主义
Demystifying the Lagrangian formalism for field theories
论文作者
论文摘要
本文扩展了以前的工作，以得出和激发Lagrangian的Lagrangian表述。在此过程中，我们采取了三个故意的步骤。首先，我们给出了动作的定义，并为现场理论提供了Euler-Lagrange方程。其次，我们证明了Euler-Lagrange方程在任意坐标转换下是独立的，并激发了这种独立性对于物理学中的现场理论是可取的。然后，我们将Lagrangian用于电动力学作为示例Lagrangian，并证明相关的Euler-Lagrange方程会导致麦克斯韦的方程式。
This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for field theories. Second, we prove the Euler-Lagrange equations are independent under arbitrary coordinate transformations and motivate that this independence is desirable for field theories in physics. We then use the Lagrangian for Electrodynamics as an example field Lagrangian and prove that the related Euler-Lagrange equations lead to Maxwell's equations.
