Title: Is the Lorenz Gauge a Choice? Gauge Freedom and the Structure of Electrodynamics Show Chinese title

Title: 洛伦兹规范是一种选择吗？ 规范自由度与电动力学的结构

Abstract: In undergraduate electromagnetism courses, the Lorenz gauge condition is often presented as a convenient mathematical choice that decouples the wave equations for the scalar and vector potentials. While true, this presentation may leave students with the impression that the condition is entirely arbitrary. This Note explores the fundamental structure of gauge invariance, demonstrating that the Lorenz condition is not an ad-hoc imposition but rather the most elegant and natural simplification afforded by the theory's inherent gauge freedom. We explicitly show how the gauge function itself transforms, proving that one can always choose a gauge in which the Lorenz condition holds. This approach aims to transform the topic from a formal trick into an instructive example of the structure of gauge theories. Show Chinese abstract

Abstract: 在本科生电磁学课程中，洛伦兹规范条件通常被介绍为一种方便的数学选择，它使标量势和矢量势的波动方程解耦。 虽然这是正确的，但这种表述可能会让学生认为该条件完全是任意的。 本文探讨了规范对称性的基本结构，证明洛伦兹条件并非临时强加的条件，而是理论固有规范自由度所提供的最优雅和自然的简化。 我们明确展示了规范函数本身的变换方式，证明总可以选择一个满足洛伦兹条件的规范。 这种方法旨在将该主题从一种形式技巧转变为规范理论结构的指导性例子。