Richard E. Harke

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An Introduction to the Mathematics of the Space-Time Algebra
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Abstract:
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Space-Time Algebra is the name given by David Hestenes to the Geometric Algebra of space-time. To start with, this is a Clifford Algebra over a four dimensional vector space endowed with the Minkowski metric. But, as the term is used here, we include derivatives in the Geometric Algebra, and linear functions and outermorphisms. The role of bivectors in the expression of Lorentz transformations is developed in some detail. Taken together, the result is a language that is well adapted to the needs of many areas of modern physics and engineering.

A remarkable example of the power of this language is found in a new theory of gravity, known as Gauge Theory Gravity, introduced by Chris Doran, Anthony Lasenby and Stephen Gull. This theory makes extensive use of the capabilities of Geometric Algebra giving it an elegant and concise expression. Unfortunatly, Geometric Algebra is not widely known. While this paper is based upon standard sources, it does bring together many useful results into a compact and convenient form. A number of proofs are added and others are expanded to make them more accessible.

Contents include: Geometric Algebra, Frames, Geometric Calculus, Linear Algebra, Functional Differentiation and the Space-Time Algebra.

[Postscript] 134k, gzip compressed

Email: Richard Harke