请求推荐从数学视角研究物理量纲分析的书籍及论文

Hey there! I’ve rounded up some top-tier resources that focus on dimensional analysis from a rigorous mathematical angle—exactly what you’re searching for:

Books #

• Dimensional Analysis by P.W. Bridgman: This is a timeless classic. Bridgman, a pioneer in the intersection of physics and mathematics, breaks down the mathematical foundations of dimensional analysis with incredible clarity, covering everything from axiomatic frameworks to practical applications. It’s a must-read for anyone wanting a deep, math-driven take on the topic.
• Scaling, Self-Similarity, and Intermediate Asymptotics by G.I. Barenblatt: This book leans into the mathematical modeling side of dimensional analysis. It uses tools from functional analysis and similarity theory to connect dimensional analysis with self-similar solutions, offering a sophisticated, math-heavy perspective that goes beyond basic applications.
• Mathematical Methods for Physicists by Arfken, Weber, and Harris: While it’s a comprehensive reference for physics-related math, its dedicated chapter on dimensional analysis delivers a systematic, mathematically rigorous treatment—including a formal proof of the Π theorem. It’s great if you want to tie the math to real-world physics contexts.

Papers #

• "Dimensional Analysis and Group Theory in Astrophysics" by S. Chandrasekhar: Chandrasekhar merges dimensional analysis with group theory here, using group representation theory to formalize how dimensions interact in physical systems. The paper’s mathematical rigor and astrophysical applications make it a standout resource.
• "On the Foundations of Dimensional Analysis" by H. Weyl: Written by one of the 20th century’s greatest mathematicians, this paper re-examines dimensional analysis from the lens of invariant theory and mathematical foundations. It’s perfect if you want to understand the underlying mathematical logic rather than just practical techniques.

Hope these resources help you dive deep into the topic!

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