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December 27, 2022


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László Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941.

This online publication is a reproduction the original lecture notes for the course “Applied Geometric Algebra” taught by Professor Tisza in the Spring of 1976.

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 sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza’s attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.

The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, ‘77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Course Curriculum

  • Chapter 1: Introduction Unlimited
  • Chapter 2: Algebraic Preliminaries Unlimited
  • Chapter 3: The Lorentz Group and the Pauli Algebra Unlimited
  • Chapter 4: Pauli Algebra and Electrodynamics Unlimited
  • Chapter 5: Spinor Calculus Unlimited
  • Supplementary Material on the Pauli Algebra Unlimited
  • Homework Assignments Unlimited
  • References Unlimited

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Massachusetts Institute of Technology