Classical and Quantum Mechanics via Lie algebras
Abstract
The goal of this book is to present classical mechanics, quantum mechanics, and statistical mechanics in an almost completely algebraic setting, thereby introducing mathematicians, physicists, and engineers to the ideas relating classical and quantum mechanics with Lie algebras and Lie groups. The book emphasizes the closeness of classical and quantum mechanics, and the material is selected in a way to make this closeness as apparent as possible. Much of the material covered here is not part of standard textbook treatments of classical or quantum mechanics (or is only superficially treated there). For physics students who want to get a broader view of the subject, this book may therefore serve as a useful complement to standard treatments of quantum mechanics. Almost without exception, this book is about precise concepts and exact results in classical mechanics, quantum mechanics, and statistical mechanics. The structural properties of mechanics are discussed independent of computational techniques for obtaining quantitatively correct numbers from the assumptions made. The standard approximation machinery for calculating from first principles explicit thermodynamic properties of materials, or explicit cross sections for high energy experiments can be found in many textbooks and is not repeated here.
 Publication:

arXiv eprints
 Pub Date:
 October 2008
 arXiv:
 arXiv:0810.1019
 Bibcode:
 2008arXiv0810.1019N
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 502 pages, including 301 references and a large index. Compared to the previous version, there are many small improvements and several new chapters: Chapters 2 and 3 covering simple quantum systems, and Chapters 1416, covering selected aspects of nonequilibrium thermodynamics