Week 14
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This requires character |
- 27. Irreducible representations / 19 April 2022 /
- 28. Discrete symmetry factorization / 21 April 2022 /
- Homework 14
- Optional
Characters. Orthogornality relations. Character tables. If you have understood character projection operators, we are set. We liked Tinkham, chapter 3, or Dresselhaus chapters 3 and 4 (early version available as lecture notes).
Symmetries simplify and improve the cycle expansions in a rather beautiful, not entirely obvious way, by factorizing cycle expansions. Read sects. 25.1 and 25.2. For a 1-d map with reflection symmetry determinants factorize into symmetric and and antisymmetric ones, and each one receives contributions from all kinds of orbits. In a not entirely obvious way. A triple home run: simpler symbolic dynamics, fewer cycles needed, much better convergence of cycle expansions. Once you master this, going back is unthinkable.
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group representation Due 26 April 2022 (note: in 1 week) |
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Discussion forum for week 14 |
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| Tell no Lie to plumbers A retired Army two-star general [who requested anonymity]: “If you raise a group of plumbers, you shouldn't be upset if they can't do theoretical physics.” |
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Character orthogonality relations experimental - doodles plus talkin' |
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Life on the boudary: help needed |