Double cover of SO(3) is SU(2)! Hurrah!
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For projective geometry and QM, I found Varadarajan's book nice. I was really into the foundations of QM back when I was a grad student. https://www.amazon.com/Geometry-Quantum-Theory-V-S-Varadarajan/dp/0387493859 …
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You might enjoy my ultra-terse intro to projective geometry, QM and special relativity, intended only to explain the meaning of the octonionic projective plane and exceptional Jordan algebra: http://math.ucr.edu/home/baez/octonions/node8.html …
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