Clifford Algebras

Clifford Algebras : A Computational Tool for Physicists

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Clifford algebras have become an indispensable tool for physicists at the cutting edge of theoretical investigations. Its applications in physics range from special relativity and the rotating top at one end of the spectrum, to general relativity and Dirac's equation for the electron at the other. Clifford algebras have become a virtual necessity in some areas of physics and their use is expanding in other areas; for example, in algebraic manipulations involving Dirac matrices in quantum thermodynamics, in Kaluza-Klein theories and dimensional renormalization theories, and in the formation of superstring theories. The book is aimed at beginning graduate physics and math students learning mathematical physics, relativity, quantum physics, or applied mathematics; and mathematical more

Product details

  • Hardback | 350 pages
  • 156 x 233.9 x 22.1mm | 671.33g
  • Oxford University Press Inc
  • New York, United States
  • English
  • New.
  • line figures
  • 0195098242
  • 9780195098242

Review quote

"A wonderful book...I have browsed through it while occupied with several other competing projects. In the process I have internalized the classification of Clifford algebras, learned how physicists use Dirac's equation, what they are doing when they talk about gauge theory, understood Hodge duality much better and so the codifferential operator. And I still have only browsed through a small portion of the text. I think we mathematicians should study [the] book to learn how to improve our own levels of exposition." --Daniel H. Gottlieb, Department of Mathematics, Purdue University..".this text will be most useful to research students and other scientists who need a satisfactory level of completeness and intellegebility to use Cliffod algebras as a computational tool."--Mathematical Reviewsshow more

Table of contents

1. A Taste of Clifford Algebra in Euclidean 3-Space ; 2. A Sample of Clifford Algebra in Minkowski 4-Space ; 3. Clifford Algebra for Flat n-Dimensional Spaces ; 4. Curved Spaces Embedded in Higher Dimensional Flat Spaces ; 5. The Use of Fock-Ivanenko 2-Vectors to Deal with Curved Spaces ; 6. The Use of Fock-Ivanenko 2-Vectors to Obtain the Schwarzschild Metric ; 7. The Exterior Derivative d and the Codifferential Operator d ; 8. Dirac's Equation for the Electron ; 9. The Kerr Metrick by an Elementary Brute Force Method ; 10. Petrov's Canonical Forms for the Weyl Tensor and Another Approach to the Kerr Metric ; 11. Matrix Representations and Classifications of Clifford Algebrasshow more