D. Hestenes - Böcker

The stupendous successes of the Dirac equation and quantum electrodynamics have established the electron as the most well understood of the fundamental constituents of matter. Nevertheless, physicists agree that the electron still has secrets to reveal. Moreover, powerful new theoretical and experimental tools for probing those secrets have been sharpened during the last decade. The 1990 Electron Workshop was organized to bring theorists and experimentalists together to discuss their common goal of knowing the electron. These Proceedings describe the present state and future prospects for progress toward that goal. The Electron presents the latest theoretical and experimental work seeking to probe the as yet undiscovered secrets of this particle. The theoretical papers encompass a wide range of views on the electron. Several argue that the zitterbewegung is more than a mathematical peculiarity of the Dirac equation, that it may well be a real physical phenomenon and so worthy of serious study both theoretically and experimentally. Besides generating the electron spin and magnetic moment, the zitterbewegung may be a vital clue to electron structure and self-interaction.Some of the papers employ a radical new formulation of the Dirac theory which reveals a hidden geometric structure in the theory that supports a zitterbewegung interpretation.

Providing an introduction to geometric algebra as a unified language for physics and mathematics, this text contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces co-ordinate-free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in government and industrial space programmes, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion. Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors.Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It should contain sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly 100 pages on relativistic mechanics. The treatment uses geometric algebra and provides a detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.

Providing an introduction to geometric algebra as a unified language for physics and mathematics, this text contains extensive applications to classical mechanics in a textbook format suitable for courses at an intermediate level. The text is supported by more than 200 diagrams to help develop geometrical and physical intuition. Besides covering the standard material for a course on the mechanics of particles and rigid bodies, the book introduces co-ordinate-free methods for rotational dynamics and orbital mechanics, developing these subjects to a level well beyond that of other textbooks. These methods have been widely applied in recent years to biomechanics and robotics, to computer vision and geometric design, to orbital mechanics in government and industrial space programmes, as well as to other branches of physics. The book applies them to the major perturbations in the solar system, including the planetary perturbations of Mercury's perihelion. Geometric algebra integrates conventional vector algebra (along with its established notations) into a system with all the advantages of quaternions and spinors.Thus, it increases the power of the mathematical language of classical mechanics while bringing it closer to the language of quantum mechanics. This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It should contain sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly 100 pages on relativistic mechanics. The treatment uses geometric algebra and provides a detailed treatment of spacetime maps, collisions, motion in uniform fields and relativistic precession. It conforms with Einstein's view that the Special Theory of Relativity is the culmination of developments in classical mechanics.

Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms.

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica­ tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.

Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms.