Classical and Quantum Mechanics via Lie algebras
by Arnold Neumaier, Dennis Westra
Publisher: arXiv 2011
Number of pages: 503
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.
Home page url
Download or read it online for free here:
by Peter B. Gilkey - Publish or Perish Inc.
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas and the Gauss-Bonnet theorem.
by Albert Tarantola - Springer
Reviews Lie groups, differential geometry, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. The theory of heat conduction and the theory of linear elastic media are studied in detail.
by Pavel Bleher, Alexander Its - Cambridge University Press
The book covers broad areas such as topologic and combinatorial aspects of random matrix theory; scaling limits, universalities and phase transitions in matrix models; universalities for random polynomials; and applications to integrable systems.
by William Elwood Byerly - Ginn and company
From the table of contents: Development in Trigonometric Series; Convergence of Fourier's Series; Solution of Problems in Physics by the Aid of Fourier's Integrals and Fourier's Series; Zonal Harmonics; Spherical Harmonics; Cylindrical Harmonics; ...