Geometric Quantization

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Clarendon Press, 1997 - Science - 307 pages
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The geometric approach to quantization was introduced by Konstant and Souriau more than 20 years ago. It has given valuable and lasting insights into the relationship between classical and quantum systems, and continues to be a popular research topic. The ideas have proved useful in pure mathematics, notably in representation theory, as well as in theoretical physics. The most recent applications have been in conformal field theory and in the Jones-Witten theory of knots. The successful original edition of this book was published in 1980. Now it has been completely revised and extensively rewritten. The presentation has been simplified and many new examples have been added. The material on field theory has been expanded.
 

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Contents

SYMPLECTIC GEOMETRY
1
LAGRANGIAN AND HAMILTONIAN MECHANICS
16
SYMMETRY
38
HAMILTONJACOBI THEORY
60
COMPLEX POLARIZATIONS
89
ELEMENTARY RELATIVISTIC SYSTEMS
107
CLASSICAL FIELDS
130
PREQUANTIZATION
155
THE METAPLECTIC CORRECTION
218
APPENDIX
257
Vector bundles
263
Distributions and foliations
269
Stationary phase
276
REFERENCES
291
INDEX OF NOTATION
301
Copyright

QUANTIZATION
171

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About the author (1997)

Dr N. M. J. Woodhouse, Wadham College, Oxford, OX1 3PN.

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