Geometric algebra for physicists
著者
書誌事項
Geometric algebra for physicists
Cambridge University Press, 2003
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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