Geometric Algebra for Physicists

The first fully self-contained introduction to geometric algebra by two leading experts in the field.

Chris Doran (Author), Anthony Lasenby (Author)

9780521715959, Cambridge University Press

Paperback, published 22 November 2007

594 pages, 82 b/w illus. 135 exercises
24.6 x 17.3 x 2.8 cm, 1.14 kg

'The range of topics presented in the book is astonishing. … The present book is intended for physicists, but mathematicians will also find it highly valuable. The exposition of Grassmann's algebra given at the beginning of the book is exceptionally clear and is written with a light touch. … It is extraordinarily well written and is a beautifully produced piece.' The Mathematical Gazette

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.

Preface
Notation
1. Introduction
2. Geometric algebra in two and three dimensions
3. Classical mechanics
4. Foundations of geometric algebra
5. Relativity and spacetime
6. Geometric calculus
7. Classical electrodynamics
8. Quantum theory and spinors
9. Multiparticle states and quantum entanglement
10. Geometry
11. Further topics in calculus and group theory
12. Lagrangian and Hamiltonian techniques
13. Symmetry and gauge theory
14. Gravitation
Bibliography
Index.

Subject Areas: Mathematical physics [PHU], Topology [PBP], Geometry [PBM]