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Commutation Relations, Normal Ordering, and Stirling Numbers
book

Commutation Relations, Normal Ordering, and Stirling Numbers

by Toufik Mansour, Matthias Schork
September 2015
Intermediate to advanced content levelIntermediate to advanced
528 pages
19h 34m
English
Chapman and Hall/CRC
Content preview from Commutation Relations, Normal Ordering, and Stirling Numbers
The Weyl Algebra, Quantum Theory, and Normal Ordering 159
5.2.7.4 Geometric Quantization
A more geometric approach to quantization is geometric quantization.Hereonestarts
from phase space, that is, a manifold Ω with a symplectic structure ω (a particular kind
of two-form); see Remark 5.13. Then prequantization gives rise to a Hermitian line bundle
L over Ω, equipped with a U(1)-connection whose curvature equals . L is called the
prequantum line bundle. The Hilbert space H
0
= L
2
, L) of square integrable sections
is called the prequantum Hilbert space. This is not yet the Hilbert space of the quantized
theory it is too big. But it is a step in the right direction. In particular, we can prequantize
classical observables: There is a map sending
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Publisher Resources

ISBN: 9781466579897