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Continue reading...I explain by simple examples (one-parameter Lie groups), partly in the original language, and along the historical papers of Sophus Lie, Abraham Cohen, and Emmy Noether how Lie groups became a central topic in physics. Physics, in contrast to mathematics, didn’t experience the Bourbakian transition so the language of for example differential geometry didn’t change quite as much during the last hundred years as it did in mathematics. This also means that mathematics at that time has been written in a way that is far closer to the language of physics, and those papers are not as old-fashioned as you might expect.
Couchyam said:It might also help to explain that the focus in math shifted to algebraic geometry and more general algebraic groups.
Couchyam said:Also, I think there might still be at least some finite, nonzero level of mathematical interest in the mysterious and unexpected connection between semi-simple Lie groups (or even just finite subgroups of SU(2)) ...
Couchyam said:... and Dynkin diagrams.
Well, there are the cyclic groups of order ##N##, dihedral groups, and the symmetries of Platonic solids, which I think McKay noticed correspond (tantalizingly) to the (possibly extended) A, D, and E Dynkin diagrams respectively.fresh_42 said:Is there another finite subgroup besides ##\{\pm 1\}##?
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC391682/pdf/pnas00617-0279.pdffresh_42 said:Is there another finite subgroup besides ##\{\pm 1\}##?
Exactly.martinbn said:
The book "When Lie Groups Became Physics" is about the history and development of Lie groups in the field of physics. It explores how these mathematical structures were first introduced and how they have been used to understand and model physical phenomena.
The author of "When Lie Groups Became Physics" is physicist and historian of science, Robert D. Purrington. He is a professor at the University of Montana and has published extensively on the history of mathematics and physics.
Lie groups are mathematical structures that describe continuous symmetries. In physics, they are used to understand and model physical systems that exhibit symmetries, such as rotations, translations, and reflections. They are important because they provide a powerful framework for understanding the laws of nature and have been applied in various areas of physics, including quantum mechanics, relativity, and particle physics.
The title "When Lie Groups Became Physics" refers to the pivotal role that Lie groups played in the development of modern physics. In the early 20th century, mathematician Sophus Lie's work on these groups provided a powerful tool for physicists to understand and describe the laws of nature. This marked a significant shift in the way physics was approached and led to major breakthroughs in the field.
Yes, "When Lie Groups Became Physics" is written in a clear and accessible style that is suitable for non-mathematicians. While some mathematical background may be helpful, the book does not assume any advanced knowledge of mathematics and provides explanations and examples to help readers understand the concepts. It is a great read for anyone interested in the history and development of physics and mathematics.