Completing Canonical Quantization. John R. Klauder University of Florida Gainesville, FL. Something Strange. L. Landau, E.M. Lifshitz, Quantum mechanics: Non-relativistic theory , 3rd ed., Pergamon Press, 1977. "Thus quantum mechanics occupies a very unusual
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Completing Canonical Quantization
John R. Klauder
University of Florida
L. Landau, E.M. Lifshitz, Quantum mechanics:
Non-relativistic theory, 3rd ed., Pergamon Press,
"Thus quantum mechanics occupies a very unusual
place among physical theories: it contains classical
mechanics as a limiting case, yet at the same time it
requires this limiting case for its own formulation."
The Principles of Quantum Mechanics
1 Classical/Quantum connection
Canonical & Affine quantization Enhanced classical theories
2 Two toy models
3 Rotationally symmetric models
Macroscopic variations of Microscopic states:
Basic state: Translated basic state: Translated Fourier state: Coherent states:
CLASSICAL MECHANICS IS QUANTUM MECHANICS RESTRICTED TO A CERTAIN TWO DIMENSIONAL SURFACE IN HILBERT SPACE
also (q < 0 , Q < 0) U (q > 0 , Q > 0)
. . .
A free theory!
a nontrivial quantization results if N is finite or N is infinite---withNOdivergences!
WHAT HAS BEEN ACCOMPLISHED ??
(8pp) (2012); arXiv:1204.2870