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Geometric Algebra for Physicists

Autor Chris Doran, Anthony Lasenby
en Limba Engleză Paperback – 21 noi 2007
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.
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Specificații

ISBN-13: 9780521715959
ISBN-10: 0521715954
Pagini: 594
Ilustrații: 82 b/w illus. 135 exercises
Dimensiuni: 173 x 246 x 28 mm
Greutate: 1.01 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

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

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Descriere

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