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Lectures on Clifford (Geometric) Algebras and Applications

Rafal Ablamowicz and Garret Sobczyk
Publisher: 
Birkhäuser
Publication Date: 
2004
Number of Pages: 
221
Format: 
Paperback
Price: 
29.95
ISBN: 
0-8176-3257-3
Category: 
Monograph
We do not plan to review this book.

 

Preface (Rafal Ablamowicz and Garret Sobczyk) * Lecture 1: Introduction to Clifford Algebras (Pertti Lounesto) * 1.1 Introduction * 1.2 Clifford algebra of the Euclidean plane * 1.3 Quaternions * 1.4 Clifford algebra of the Euclidean space R3 * 1.5 The electron spin in a magnetic field * 1.6 From column spinors to spinor operators * 1.7 In 4D: Clifford algebra Cl4 of R4 * 1.8 Clifford algebra of Minkowski spacetime * 1.9 The exterior algebra and contractions * 1.10 The Grassmann–Cayley algebra and shuffle products * 1.11 Alternative definitions of the Clifford algebra * 1.12 References * Lecture 2: Mathematical Structure of Clifford Algebras (Ian Porteous) * 2.1 Clifford algebras * 2.2 Conjugation * 2.3 References * Lecture 3: Clifford Analysis (John Ryan) * 3.1 Introduction * 3.2 Foundations of Clifford analysis * 3.3 Other types of Clifford holomorphic functions * 3.4 The equation Dkƒ  = 0 * 3.5 Conformal groups and Clifford analysis * 3.6 Conformally flat spin manifolds * 3.7 Boundary behavior and Hardy spaces * 3.8 More on Clifford analysis on the sphere * 3.9 The Fourier transform and Clifford analysis * 3.10 Complex Clifford analysis * 3.11 References * Lecture 4: Applications of Clifford Algebras in Physics (William E. Baylis) * 4.1 Introduction * 4.2 Three Clifford algebras * 4.3 Paravectors and relativity * 4.4 Eigenspinors * 4.5 Maxwell's equation * 4.6 Quantum theory * 4.7 Conclusions * 4.8 References * Lecture 5: Clifford Algebras in Engineering (J.M. Selig) * 5.1 Introduction * 5.2 Quaternions * 5.3 Biquaternions * 5.4 Points, lines, and planes * 5.5 Computer vision example * 5.6 Robot kinematics * 5.7 Concluding remarks * 5.8 References * Lecture 6: Clifford Bundles and Clifford Algebras (Thomas Branson) * 6.1 Spin Geometry * 6.2 Conformal Structure * 6.3 Tractor constructions * 6.4 References * Appendix (Rafal Ablamowicz and Garret Sobczyk) * 7.1 Software for Clifford algebras * 7.2 References * Index





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Algebra

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