Geometric Algebra for Physicists

This book is a complete guide to the current state of geometric algebra with early chapters providing a self-contained introduction. Topics range from new techniques for handling rotations in arbitrary dimensions, the links between rotations, bivectors, the structure of the Lie groups, non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. 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. "This book will be of interest to researchers working in the fields of geometry, relativity and quantum theory. It can also be used as a text for advanced undergraduates and graduate courses on the physical applications of geometric algebra."--Jacket The goal of expressing geometrical relationships through algebraic equations has dominated much of the development of mathematics. First fully self-contained introduction to geometric algebra by two leading experts in the field Chris Doran And Anthony Lasenby. Includes Bibliographical References (p. 568-574) And Index.