UID:
almafu_9959239888202883
Format:
1 online resource (xiv, 578 pages) :
,
digital, PDF file(s).
ISBN:
1-316-08478-7
,
1-139-63593-X
,
1-139-64869-1
,
1-139-64108-5
,
1-139-63824-6
,
0-511-80749-X
Content:
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.
Note:
First paperback edition published 2007.
,
4th printing 2010.
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Cover; Title Page; Copyright; Contents; Preface; Notation; 1Introduction; 1.1 Vector (linear) spaces; 1.2 The scalar product; 1.3 Complex numbers; 1.4 Quaternions; 1.5 The cross product; 1.6 The outer product; 1.7 Notes; 1.8 Exercises; 2Geometric algebra in two and three dimensions; 2.1 A new product for vectors; 2.2 An outline of geometric algebra; 2.3 Geometric algebra of the plane; 2.4 The geometric algebra of space; 2.5 Conventions; 2.6 Reflections; 2.7 Rotations; 2.8 Notes; 2.9 Exercises; 3Classical mechanics; 3.1 Elementary principles; 3.2 Two-body central force interactions
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3.3 Celestial mechanics and perturbations3.4 Rotating systems and rigid-body motion; 3.5 Notes; 3.6 Exercises; 4Foundations of geometric algebra; 4.1 Axiomatic development; 4.2 Rotations and reflections; 4.3 Bases, frames and components; 4.4 Linear algebra; 4.5 Tensors and components; 4.6 Notes; 4.7 Exercises; 5Relativity and spacetime; 5.1 An algebra for spacetime; 5.2 Observers, trajectories and frames; 5.3 Lorentz transformations; 5.4 The Lorentz group; 5.5 Spacetime dynamics; 5.6 Notes; 5.7 Exercises; 6Geometric calculus; 6.1 The vector derivative; 6.2 Curvilinear coordinates
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6.3 Analytic functions6.4 Directed integration theory; 6.5 Embedded surfaces and vector manifolds; 6.6 Elasticity; 6.7 Notes; 6.8 Exercises; 7Classical electrodynamics; 7.1 Maxwell's equations; 7.2 Integral and conservation theorems; 7.3 The electromagnetic field of a point charge; 7.4 Electromagnetic waves; 7.5 Scattering and diffraction; 7.6 Scattering; 7.7 Notes; 7.8 Exercises; 8Quantum theory and spinors; 8.1 Non-relativistic quantum spin; 8.2 Relativistic quantum states; 8.3 The Dirac equation; 8.4 Central potentials; 8.5 Scattering theory; 8.6 Notes; 8.7 Exercises
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9Multiparticle states and quantum entanglement9.1 Many-body quantum theory; 9.2 Multiparticle spacetime algebra; 9.3 Systems of two particles; 9.4 Relativistic states and operators; 9.5 Two-spinor calculus; 9.6 Notes; 9.7 Exercises; 10Geometry; 10.1 Projective geometry; 10.2 Conformal geometry; 10.3 Conformal transformations; 10.4 Geometric primitives in conformal space; 10.5 Intersection and reflection in conformal space; 10.6 Non-Euclidean geometry; 10.7 Spacetime conformal geometry; 10.8 Notes; 10.9 Exercises; 11Further topics in calculus and group theory; 11.1 Multivector calculus
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11.2 Grassmann calculus11.3 Lie groups; 11.4 Complex structures and unitary groups; 11.5 The general linear group; 11.6 Notes; 11.7 Exercises; 12Lagrangian and Hamiltonian techniques; 12.1 The Euler-Lagrange equations; 12.2 Classical models for spin-1/2 particles; 12.3 Hamiltonian techniques; 12.4 Lagrangian field theory; 12.5 Notes; 12.6 Exercises; 13Symmetry and gauge theory; 13.1 Conservation laws in field theory; 13.2 Electromagnetism; 13.3 Dirac theory; 13.4 Gauge principles for gravitation; 13.5 The gravitational field equations; 13.6 The structure of the Riemann tensor; 13.7 Notes
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13.8 Exercises
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English
Additional Edition:
ISBN 0-521-71595-4
Additional Edition:
ISBN 0-521-48022-1
Language:
English
URL:
https://doi.org/10.1017/CBO9780511807497
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