AI 中文总结
研究认为量纲分析是一种规范理论，通过李群等性质引出量演算，借助规范群选择理解测量尺度分类，还重新诠释白金汉-Π定理，让计算‘Π’数量成为不变量理论问题。
AI 中文摘要
我认为量纲分析可恰当地被视为一种规范理论。此观点通过李群、李代数及表示理论的固有性质自然引出常用的量演算。规范理论解释对于非常数单位可能最为有力。我解释了如何通过不同规范群的选择来理解史蒂文斯的测量尺度分类。最后，我以一种也适用于典型规范理论的方式重新诠释和表述了白金汉-Π定理。计算‘Π’的数量成为不变量理论中一个著名问题。
英文摘要
I argue that dimensional analysis can appropriately be thought of as a gauge theory. This picture naturally leads to the usual quantity calculus through inherent properties of Lie groups, Lie algebras, and representation theory. The gauge theory interpretation is perhaps strongest for non-constant units. I explain how Stevens's classification of scales of measurement can be understood by choices of different gauge groups. Finally, I reinterpret and rephrase the Buckingham-Π Theorem in a way that also applies to typical gauge theories. Counting the number of ''Π''s becomes a well-known problem of invariant theory.
Comments55 pages, comments are welcome!
