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
- Overview of Math
- Overview of Classical mechanics
- Overview of the Theory of Relativity
- Overview of Relativistic Electromagnetic Theory in Covariant Form
- Overview of Lie Algebras & Groups
- The Heisenberg group – Foundations of quantum theory
- The Harmonic Oscillator group
- The Rotation group O3 = SU2
- The Lorentz group – particle theory
- The Poincare group – particle theory
- XPM group – relativistic position operators
- Internal Symmetry – SUn
- TCP & discrete symmetry groups
- The General Linear & Affine Group
- The DeSitter Group
- The Markov Group
- Foundations of Lie Algebras and Lie Groups
- Course Summary and Conclusions
- Applications of the Markov group to Fibonacci numbers
- Applications of the Markov group to Logic, Numbers, & Information
- Network Theory
- Applications of Information theory to Quantum Theory
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*IMPORTANT*
NOTES WILL BE UPLOADED BY 8/20 EVENING. SORRY FOR THE INCONVENIENCE!