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Geometric Algebra for Physicists

  • Date Published: November 2007
  • availability: Available
  • format: Paperback
  • isbn: 9780521715959

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About the Authors
  • 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.

    • The only fully self-contained introduction to geometric algebra including applications in relativistic physics and gravitation
    • The first full account of the geometric algebra approach to multiparticle quantum physics and supersymmetry
    • A book written by two authors who have shaped the subject in the last decade
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    Reviews & endorsements

    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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    Product details

    • Date Published: November 2007
    • format: Paperback
    • isbn: 9780521715959
    • length: 594 pages
    • dimensions: 246 x 173 x 28 mm
    • weight: 1.14kg
    • contains: 82 b/w illus. 135 exercises
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Chris Doran, University of Cambridge
    Chris Doran obtained his PhD from the University of Cambridge, having gained a distinction in Part II of his undergraduate degree. He was elected a Junior Research Fellow of Churchill College, Cambridge in 1993, was made a Lloyd's of London Fellow in 1996 and was the Schlumberger Interdisciplinary Research Fellow of Darwin College, Cambridge in 1997 and 2000. He is currently a Fellow of Sidney Sussex College, Cambridge and holds an EPSRC Advanced Fellowship. Dr Doran has published widely on aspects of mathematical physics and is currently researching applications of geometric algebra in engineering and computer science.

    Anthony Lasenby, University of Cambridge
    Anthony Lasenby is Professor of Astrophysics and Cosmology at the University of Cambridge, and is currently Head of the Astrophysics Group and the Mullard Radio Astronomy Observatory in the Cavendish Laboratory. He began his astronomical career with a PhD at Jodrell Bank, specialising in the Cosmic Microwave Background, which has been a major subject of his research ever since. After a brief period at the National Radio Astronomy Observatory in America, he moved from Manchester to Cambridge in 1984, and has been at the Cavendish since then. He is the author or coauthor of nearly 200 papers spanning a wide range of fields, from early universe cosmology to computer vision. His introduction to geometric algebra came in 1988, when he encountered the work of David Hestenes for the first time, and since then he has been developing geometric algebra techniques and employing them in his research in many areas.

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