Description
This book is a guide to the current state of geometric algebra, which has applications in physics and engineering. It covers topics such as rotations in arbitrary dimensions, the links between rotations, bivectors and the structure of the Lie groups, and later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. The book 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.
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.
Review:
Review of the hardback: 'I would therefore highly recommend this book for anyone wishing to enter this interesting and potentially fundamental area.' Mathematics Today '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
Related Products
