https://www.chenk.top/zh/tags/fiber-bundles/Recent content in Fiber-Bundles on Chen Kai BlogHugozh-CNTue, 23 Nov 2021 09:00:00 +0000https://www.chenk.top/zh/differential-geometry/12-%E7%BA%A4%E7%BB%B4%E4%B8%9B%E4%B8%8E%E7%89%A9%E7%90%86/Tue, 23 Nov 2021 09:00:00 +0000https://www.chenk.top/zh/differential-geometry/12-%E7%BA%A4%E7%BB%B4%E4%B8%9B%E4%B8%8E%E7%89%A9%E7%90%86/<p>高中物理课讲电磁学时，老师写过一个让人记忆深刻的公式：<span class="math-inline">$\vec{E} = -\nabla\phi - \partial_t\vec{A}$</span> ，<span class="math-inline">$\vec{B} = \nabla\times\vec{A}$</span> 。电磁场由一个标量势 <span class="math-inline">$\phi$</span> 和一个向量势 <span class="math-inline">$\vec{A}$</span> 决定。但同一个老师当时说了一句奇怪的话：&quot;<span class="math-inline">$\phi$</span> 和 <span class="math-inline">$\vec{A}$</span> 不是唯一的——你可以做<em>规范变换</em> <span class="math-inline">$\phi \to \phi - \partial_t\lambda$</span> , <span class="math-inline">$\vec{A} \to \vec{A} &#43; \nabla\lambda$</span> ，电磁场不变。这种自由叫&rsquo;规范不变性&rsquo;。&quot;</p>