Applied Geometric Algebra (Tisza)

by László Tisza

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Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These course notes attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools.

Description from LibreTexts.

Publisher
Massachusetts Institute of Technology
Subjects
Mathematics, Abstract and Geometric Algebra
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Introduction to Applied Geometric Algebra
  5. Table of Contents
  6. Licensing
  7. 1: Algebraic Preliminaries
  8. 1.1: Groups
  9. 1.2: The geometry of the three-dimensional rotation group. The Rodrigues-Hamilton theorem
  10. 1.3: The n-dimensional vector space V(n)
  11. 1.4: How to multiply vectors? Heuristic considerations
  12. 1.5: A short survey of linear groups
  13. 1.6: The unimodular group SL(n, R) and the invariance of volume
  14. 1.7: On “alias” and “alibi”. The Object Group
  15. 2: The Lorentz Group and the Pauli Algebra
  16. 2.1: Introduction to Lorentz Group and the Pauli Algebra
  17. 2.2: The Corpuscular Aspects of Light
  18. 2.3: On Circular and Hyperbolic Rotations
  19. 2.4: The Pauli Algebra
  20. 3: Pauli Algebra and Electrodynamics
  21. 3.1: Lorentz Transformation and Lorentz force
  22. 3.2: The Free Maxwell Field
  23. 4: Spinor Calculus
  24. 4.1: From triads and Euler angles to spinors. A heuristic introduction
  25. 4.2: Rigid Body Rotation
  26. 4.3: Polarized light
  27. 4.4: Relativistic triads and spinors. A preliminary discussion
  28. 4.5: Review of SU(2) and preview of quantization
  29. 5: Supplementary Material on the Pauli Algebra
  30. 5.1: Useful formulas
  31. 5.2: Lorentz invariance and bilateral multiplication
  32. 5.3: Typical Examples
  33. 5.4: On the us of Involutions
  34. 5.5: On Parameterization and Integration
  35. 6: Problems
  36. 6.1: Problems
  37. Back Matter
  38. References
  39. Index
  40. Glossary
  41. Detailed Licensing