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Clifford (Geometric) Algebras: with applications to physics, mathematics, and engineering

Autor William E. Baylis
en Limba Engleză Hardback – 22 aug 1996
This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas­ sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.
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Specificații

ISBN-13: 9780817638689
ISBN-10: 0817638687
Pagini: 517
Ilustrații: XVIII, 517 p.
Dimensiuni: 178 x 254 x 30 mm
Greutate: 1.16 kg
Ediția:1996
Editura: Birkhäuser Boston
Colecția Birkhäuser
Locul publicării:Boston, MA, United States

Public țintă

Research

Cuprins

1 Introduction.- 2 Clifford Algebras and Spinor Operators.- 3 Introduction to Geometric Algebras.- 4 Linear Transformations.- 5 Directed Integration.- 6 Linear Algebra.- 7 Dynamics.- 8 Electromagnetism.- 9 Electron Physics I.- 10 Electron Physics II.- 11 STA and the Interpretation of Quantum Mechanics.- 12 Gravity I — Introduction.- 13 Gravity II — Field Equations.- 14 Gravity III — First Applications.- 15 Gravity IV — The ‘Intrinsic’ Method.- 16 Gravity V — Further Applications.- 17 The Paravector Model of Spacetime.- 18 Eigenspinors in Electrodynamics.- 19 Eigenspinors in Quantum Theory.- 20 Eigenspinors in Curved Spacetime.- 21 Spinors: Lorentz Group.- 22 Spinors: Clifford Algebra.- 23 Genersd Relativity: An Overview.- 24 Spinors in General Relativity.- 25 Hypergravity I.- 26 Hypergravity II.- 27 Properties of Clifford Algebras for Fundamental Particles.- 28 The Extended Grassmann Algebra of R3.- 29 Geometric Algebra: Applications in Engineering.- 30 Projective Quadrics, Poles, Polars, and Legendre Transformations.- 31 Spacetime Algebra and Line Geometry.- 32 Generalizations of Clifford Algebra.- 33 Clifford Algebra Computations with Maple.

Recenzii

"Of interest due to the many provocative physical interpretations of quantum mechanics and gravitational theory suggested by the Clifford algebra approach to these theories."
—Mathematical Reviews