Lie Groups And Lie Algebras

Classical mechanics, one of the oldest branches of science, has undergone a long evolution, developing hand in hand with many areas of mathematics, including calculus, differential geometry, and the theory of Lie groups and Lie algebras. The modern formulations of Lagrangian and Hamiltonian mechanics, in the coordinate-free language of differential geometry, are elegant and general.

Knowledge of an analytic group implies knowledge of its module category. However complete knowledge of the category does not determine the group. Professor Magid shows here that the category determines another, larger group and an algebra of functions in this new group.

Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context. Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The book also includes exercises and proofed examples to test the students' understanding of the various concepts, as well as to extend the text's themes.

Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context.