Geometric QuantizationClarendon Press, 1992 - 307 Seiten 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. |
Inhalt
SYMPLECTIC GEOMETRY | 1 |
COMPLEX POLARIZATIONS | 5 |
LAGRANGIAN AND HAMILTONIAN MECHANICS | 16 |
SYMMETRY | 38 |
HAMILTONJACOBI THEORY | 60 |
ELEMENTARY RELATIVISTIC SYSTEMS | 107 |
CLASSICAL FIELDS | 130 |
PREQUANTIZATION | 138 |
8 | 205 |
THE METAPLECTIC CORRECTION | 218 |
APPENDIX | 257 |
Vector bundles | 263 |
Distributions and foliations | 269 |
Stationary phase | 276 |
| 291 | |
| 301 | |
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Häufige Begriffe und Wortgruppen
canonical coordinates canonical transformations Cauchy surface classical coadjoint cocycle coisotropic complex structure components condition conjugate connection constant constraint construction coordinate system corresponding cotangent bundle curvature defined denote derivative determined diffeomorphism element example Əqa fibres field equations Fock space foliation follows geometric given Guillemin and Sternberg Hamiltonian vector fields hence Hilbert space holomorphic inner product integral curves invariant Kähler Lagrangian submanifold Lagrangian subspace Lie algebra line bundle linear metaplectic metric momentum neighbourhood nonnegative orbits pairing particle phase space polarized sections positive projection pull-back quantization quantum real polarization reduction representation scalar solutions spanned spinor square root symmetric symplectic form symplectic manifold symplectic potential symplectic structure symplectic vector space tensor theory time-dependent transition functions trivial unitary values vanishes vector bundle vector space Vp(M wave functions
Verweise auf dieses Buch
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics Robert M. Wald Eingeschränkte Leseprobe - 1994 |
Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time ... Roger Penrose,Wolfgang Rindler Eingeschränkte Leseprobe - 1984 |