- Spacetime Algebra (STA) provides a unified, coordinate-free mathematical framework for both classical and quantum physics
- STA reduces electrodynamics to a single Maxwell equation with explicit kinship to Dirac's equation
- STA reveals hidden geometric structure in Dirac’s equation with new insight into the role of complex numbers in quantum mechanics
- STA offers a novel gauge theory approach to quantum mechanics and General Relativity
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- About this book
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This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future.
At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas.
These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible.
There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘Space-Time Algebra’, despite its short length, and some of them are effectively still research topics for the future.
From the Foreward by Anthony Lasenby
- Table of contents (5 chapters)
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Geometric Algebra
Pages 1-24
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Electrodynamics
Pages 25-33
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Dirac Fields
Pages 35-45
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Lorentz Transformations
Pages 47-61
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Geometric Calculus
Pages 63-85
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Table of contents (5 chapters)
- Download Preface 1 PDF (155.1 KB)
- Download Sample pages 2 PDF (188.9 KB)
- Download Table of contents PDF (109.3 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Space-Time Algebra
- Authors
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- David Hestenes
- Copyright
- 2015
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer International Publishing Switzerland
- eBook ISBN
- 978-3-319-18413-5
- DOI
- 10.1007/978-3-319-18413-5
- Hardcover ISBN
- 978-3-319-18412-8
- Softcover ISBN
- 978-3-319-38688-1
- Edition Number
- 2
- Number of Pages
- XXIV, 102
- Additional Information
- Originally published by Gordon and Breach Science Publishers, New York, 1966
- Topics
