电磁学的几何代数简化方法
A simplified approach to electromagnetism using geometric algebra
摘要：
提出了一种新的简化电磁学教学方法，该方法采用几何代数（GA）的形式，不需要向量演算或张量指数表示法，从而使学生更容易理解。提出的四维时空在空间和时间维度之间是完全对称的，因此实现了闵可夫斯基最初的设想。为了提高学生的接受度，我们还专注于力和能量能量守恒和动量，这在GA中采取非常简单的形式，使学生可以很容易地建立在使用这些法律开发的直觉从研究牛顿力学。潜在的配方也集成到演示文稿中，允许一个替代的解决方案的路径，以及介绍拉格朗日方法。文中对几个问题进行了阐述，以明确其实施过程。我们扩展了以前的治疗这一领域，通过包括潜在的制定，能量守恒和动量，磁单极子的推广，以及简化以前报道的结果，通过消除时空度量的需要。
英文摘要：
A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for students. The four-dimensional spacetime proposed is completely symmetrical between the space and time dimensions, thus fulfilling Minkowski's original vision. In order to improve student reception we also focus on forces and the conservation of energy and momentum, which take a very simple form in GA, so that students can easily build on established intuitions in using these laws developed from studying Newtonian mechanics. The potential formulation is also integrated into the presentation that allows an alternate solution path, as well as an introduction to the Lagrangian approach. Several problems are solved throughout the text to make the implementation clear. We extend previous treatment of this area, through including the potential formulation, the conservation of energy and momentum, the generalization for magnetic monopoles, as well as simplifying previously reported results through eliminating the need for the spacetime metric.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
