Mathematical Physics: A Modern Introduction to its Foundations

by Sadri Hassani

The goal of this book is to expose the reader to the indispensable role that mathematics plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics.

Genres: Physics, Mathematics, Science, Reference

Paperback

First published December 21, 1998

Reviews

[Javad Ebadi · Rating 4 out of 5]

I've read some parts of this book. It is more like mathematics books. Sometimes there are many definitions and developments of the subjects which are unnecessary for physicists. However, if a physicist likes or needs abstract and solid foundation of a the mathematics he or she uses, then this book is absolutely useful.