Emmy Noether’s Wonderful Theorem

http://www.springerlink.com/content/m500g70515681003/fulltext.pdf

[1]http://dx.doi.org/10.1063/PT.3.1263

48p

In constrast to Hamilton's principle, relativistic mechanics postulates that, of all world lines through spacetime that a freely falling particle might follow from even A to even ZB, the world line actually followed is the one for which the elapsed proper time is a maximum. Let us call this "Fermat's principle for relativistic partivles. It has been enormously successful, for example, in predicting gravitational redshfit, precession of orbit perihelion, deflection of starlight, gravitational lensing, and the relativistic precession of gyroscopes.

50p constrained Lagrangian http://farside.ph.utexas.edu/teaching/336k/newton/node90.html Lagrange multiplier method ?

79p "Adiabatic invariance" refers to situations where the system parameters are slowly changed, such that the product of two quantities is approximately conserved, even though the two quantities themselves are not separately conserved. Perhaps the most cited example arises in the simple pendulum whose length slowly changes. The energy E of the pendulum does not stay constant, because of the work performed on it.

(...) Therefore the adiabatic invariance and the close-path abbreviated action are synonymous. The adiabatic invariance of the abbreviated action formed the foundation of the pre-wave-mechanics "old quantum theory" of 1913-26. Periodic systems wer quantized by invoking the Bohr-Sommerfeld-Wilson quantization postulate, illustrated here for one-dimensional motion.../n