NONLINEAR DYNAMICS: QUANTUM CHAOS  
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	Georgia Tech PHYS 7224			Spring semester 2002  
	Predrag Cvitanovic'

	Lecture 25         Thu, Apr 9 2002 12:05-13:25 in Howey S106


Discrete symmetries 
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In this unplanned lecture on symmetries I diverged far
from the ChaosBook text. Here is some reading to
supplement the lecture:

Reading:
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	Group Theory
        ---    www.nbi.dk/GroupTheory/postscript.html

chapter  5 - Permutations
	 sects. 5.1, 5.2
chapter  8 - Unitary groups
	 sects. 8.1, 8.2

	Lattice Field Theory
	---  www.nbi.dk/~predrag/field_the/lattFT/lattFT.ps.gz
sect. 1.5 Discrete Fourier transforms 
	 (as examples of the full reduction of the cyclic group
	  - a subgroup of the permutation group)
	
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The solution of problems starting with helium trajectories and ending with
the helium spectrum form the final exam in the course. 

If you prefer, 
you can compute the 3-disk resonances instead, the determination
of perioidc orbits is easier in billards than it is in the flows.
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