: These are groups that are also smooth manifolds, with the group operations being smooth. Lie groups are crucial in physics for describing continuous symmetries. Examples include the rotation group SO(3), the Lorentz group SO(1,3), and the unitary group U(n).
, is a widely acclaimed textbook that bridges abstract mathematical structures with their profound applications in physical reality. First published in 1994, the book is designed for senior undergraduates and graduate students, offering a cohesive treatment of symmetries across various scales of physics. Amazon.com Core Themes and Content group theory and physics sternberg pdf
What sets this apart? Sternberg immediately links representations to quantum mechanics. By Chapter 3, he is already discussing how the rotation group SO(3) forces the quantization of angular momentum. He doesn’t just state the algebra; he derives it from the group’s topology. : These are groups that are also smooth