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College of Arts & Sciences
Advanced Solutions Group

Physics 729

*NOTES WILL BE HERE SOON* This is a one semester course for PhD level Physics majors that have already taken the primary graduate physics courses in classical, quantum, and electromagnetic theory. It develops the theories of relativity, quantum theory and field theory, and internal symmetries using Lie algebras and groups. It is a one semester course that develops the representations of the Heisenberg, Rotation, Lorentz, Poincare, Unitary (internal symmetry groups), Markov & general linear group and related physics including discrete symmetries and second quantization – all from the Lie group theory and Lie algebra point of view.

Instructor: Joseph E. Johnson, PhD


Topics Covered in This Course

  1. Overview of Math
  2. Overview of Classical mechanics
  3. Overview of the Theory of Relativity
  4. Overview of Relativistic Electromagnetic Theory in Covariant Form
  5. Overview of Lie Algebras & Groups
  6. The Heisenberg group – Foundations of quantum theory
  7. The Harmonic Oscillator group 
  8. The Rotation group O3 = SU2 
  9. The Lorentz group – particle theory
  10. The Poincare group – particle theory
  11. XPM group – relativistic position operators
  12. Internal Symmetry – SUn 
  13. TCP & discrete symmetry groups
  14. The General Linear & Affine Group
  15. The DeSitter Group
  16. The Markov Group
  17. Foundations of Lie Algebras and Lie Groups
  18. Course Summary and Conclusions
  19. Applications of the Markov group to Fibonacci numbers
  20. Applications of the Markov group to Logic, Numbers, & Information
  21. Network Theory
  22. Applications of Information theory to Quantum Theory



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