Woodhouse N.M.J. — Geometric quantization :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Woodhouse N.M.J. — Geometric quantization

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Geometric quantization

Автор: Woodhouse N.M.J.

Аннотация:

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.

Язык:

Рубрика: Физика/Квантовая механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1997

Количество страниц: 307

Добавлена в каталог: 09.10.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(M, \omega)$       1
$(V, \omega)$       1
$(X, \xi)$       244
$(\mathcal{M}, \Omega)$       247
$(\mu, \mu')$       223
$Ad_{g}$       50
$B_{P}$       233
$C^{p}(\mathcal{U})$ , $Z^{p}(\mathcal{U})$ , $H^{p}(\mathcal{U})$       272
$C^{\infty}(M)$ , $C^{\infty}_{\mathds{C}}(M)$       258
$C_{P}^{\infty}(M)$       92 269
$C_{V}^{\infty}(U)$       264
$C_{\ bc}^{a}$       44
$F_{u}$       18
$g_{123}$       228
$G_{f}$ , $\mathcal{G}_{f}$ , $(G_{f})_{0}$       53
$G_{\mathds{C}}$       105
$H^{k}(M, \overline{P}, B)$       250
$H_{\mu}$ , $H_{\mu}^{\pm}$       148
$j_{a}$ , $\phi^{a}$       75
$j_{i}$       74
$K(q, z, \bar{z})$       96
$K_{J}$ , $K_{P}$       223
$K_{P}$       185
$L \otimes L'$       267
$L^{*}, \overline{L}, L^{n}, \surd L$       267
$L^{+}V$       93
$L_{A}$ , $R_{A}$       50
$L_{\ B}^{A}$       108
$MP(V, \omega)$       224
$MW_{f}$       58
$N, N^{\pm}$       148
$p_{a}$ , $q^{b}$       6 19
$R^{a}_{\ bcd}, R_{ab}, R$       263
$R_{t}$       138
$S, S^{*}, \overline{S}, \overline{S^{*}}$       108
$SL(2, \mathbb{R})$       53
$SP(n, \mathbf{R})$       5
$SP(n, \mathds{C})$       5
$SP(V, \omega)$       5
$S^{a}$       115
$S_{P}^{k}(U)$       77 92
$T\bar{Q}$       25
$T^{(ab...c)}, T^{[ab...c]}$       257
$T_{\mathds{C}}M$ , $T^{*}_{\mathds{C}}M$       258
$U_{J}$       224
$V \oplus V', V \otimes V', V^{*}$       263
$V(M), V_{\mathds{C}}(M)$       258
$V\mid_{M^{'}}$ , $V_{M^{'}}$       265
$V^{H}(M)$       10
$V^{H}_{\mathds{C}}(M)$       11
$V^{LH}(M)$       10
$V^{LH}_{\mathds{C}}(M)$       11
$V_{(J)}$       257
$V_{P}(M)$       269
$V_{\mathds{C}}$       257
$X^{a}$ , $Y_{b}$       3
$X_{F}$       9
$X_{\alpha}$ , $Y_{\alpha}$ , $Z_{\alpha}$       104
$z = (z^{ab})$       93
$z_{\alpha}$       221
$\alpha |_{N}$       260
$\alpha$       268
$\bar{f}$       186 251
$\bar{i}$       26
$\bar{Q}$       25
$\bar{\rho}$       219
$\bar{\rho}_{t}$       186
$\bot$       2
$\chi$       242
$\chi_{\alpha\beta\gamma}$       219
$\delta_{P}$       186 232
$\epsilon$       156
$\epsilon_{AB}$       108
$\hat{f}$       157 162 250
$\hat{\rho}$       163
$\hat{\rho}_{tt'}$       164
$\kappa$       199
$\lambda\phi^{4}$       207
$\lambda_{g}$ , $\rho_{g}$       50
$\langle\cdot, \cdot\rangle$       156 162
$\mathbf{PF}$ , $\mathbf{F}$       221 225
$\mathcal{B}$ , $\chi$       244
$\mathcal{F}$       248
$\mathcal{G}$       38
$\mathcal{G}_{\mathds{C}}$       104
$\mathcal{L}_{X}$       259
$\mathcal{L}_{Z}$       185
$\mathcal{T}$       104
$\mu(J)$       223
$\nabla$       67 130 185
$\nabla$ , $\nabla_{X}$       264
$\omega$       6 197
$\omega^{a}$       133
$\Omega^{n}$       5
$\Omega^{p}(M)$ , $\Omega_{\mathds{C}}^{p}(M)$       259
$\omega_{L}$       17
$\overline{M}$       120
$\overline{V}$       258
$\partial_{t}X$       261
$\partial_{t}\alpha$       262
$\Phi$       212
$\phi^{\alpha}$       130
$\psi^{\pm}$       147
$\psi_{Z}$       174
$\rfloor$       259
$\rho_{*}$ , $\rho^{*}$       260
$\rho_{*}P$ , $\rho^{*}P^{'}$       270
$\rho_{tt^{'}}$       262
$\rho_{t}$       261
$\rho_{\ast}$       113
$\Sigma$       200
$\tau_{123}$       214
$\Theta$ , $\Omega$       246
$\Theta', \Omega'$       247
$\theta_{0}$       166
$\theta_{f}$ , $\omega_{f}$       51
$\theta_{L}$       18
$\tilde{B}_{\Lambda}$       241
$\tilde{F}_{J}$       224
$\tilde{X}$       261
$\triangle$ , $\surd\triangle_{\Lambda}$       236
$\triangle_{F}$       209
$\triangle_{f}^{+}$ , $\triangle_{f}^{-}$       105
$\triangle_{Q}$       185
$\triangle_{\alpha\beta}$       214
$\wedge^{p}V$       257
A      197
Action variables      74 242
Adjoint action      50
Adjoint representation      43
Aharonov — Bohm effect      188
Angle variables      75 242
Anti-unitary operator      165
Anticanonical transformations      56 121 165
Anticommutation relations      216
Antiparticle      120
B      158
Bargmann transform      196
Berry's phase      225 243
Bivectors      111
Bivectors, self-dual      111
BKS construction      202
Bohr — Sommerfeld condition      201
Bohr — Sommerfeld condition, corrected      201 241 249
Borel subgroup      105
Borel — Weil theorem      176
Bosons      176
C      120
Canonical 1-form      6 19
Canonical 2-form      6 19

Canonical bundle      223
Canonical bundle of a distribution      270
Canonical coordinates      8
Canonical coordinates, adapted to a polarization      71
Canonical diffeomorphism      8 63
Canonical flow      9
Canonical quantization      187
Canonical transformation      62—63
Canonical transformation, linear      5 63
Canonically conjugate variables      15
Caustic singularity      201
Cech cohomology      271
Characteristic distribution      12
Charge conjugation      120
Charge quantization      187
Charged symplectic structure      36 187
Chern class      161
Chern class of a complex manifold      235
Circle action      48
Classical observable      9
Coadjoint action      50 52
Coadjoint orbit      51
Coboundary      271
Coboundary Lie algebra      40
Coboundary operator      271
Cochain      271
Cocycle      271
Cocycle Lie algebra      40
Cocycle of a pairing or embedding      275
Cocycle relations      266
Coherent states      174 178—180
Cohomological wave functions      249
Cohomology group      272
Cohomology group, holomorphic      272
Coisotropic foliation      66
Coisotropic section      100
Coisotropic submanifold      13
Coisotropic subspace      2 4
Compact group      103 176
Complete vector field      261 262
Complex conjugate vector bundle      264
Complex conjugate vector space      258
Complex distribution      269
Complex distribution, integrable      270
Complex manifold      270
Complex structure      257
Complex structure, compatible with $\omega$       89
Complex structure, positive      89
Composite system      57
Configuration space      16
Connection      264
Connection form      268
Constraint      13 28
Constraint Dirac — Bergmann theory      34
Constraint first class      13
Constraint holonomic      28 31
Constraint in a Humiltoian system      31
Constraint instantaneous      30
Constraint nonholonomic      28
Constraint primary      20 34
Constraint quantization      182
Constraint second class      13
Constraint secondary      35
Contraction      259
Cotangent bundle      68 165
Covariant derivative of a spinor      111
CR structure      102
Curvature      265
D, E      66 91
D, L      250
Darboux's theorem      6
De Rham isomorphism      273
density      258
Determinant bundle      223
Differential form time-dependent      262
Differential form type (r, s)      270
Differential form with values in V      264
Dirac equation      149
Direct sum of vector bundles      263
Distribution, integrable      269
Distribution, involutive      269
Distribution, real      269
Distributional wave function      238
Dolbeault isomorphism      274
Dual bundle      263
e      130
Einstein conventions      3
Einstein's equations      143
electromagnetic field      82 134
Elementary systems      49 169
Energy      120
Energy-momentum tensor      140
Equivalence of vector bundles      264
Euclideanization      205
f      220
Feynman expansion      205
Fibre      263
Field      130
Field equation, massless      193
Flag manifold      106
Flag manifold, flat connection      100
Flow of a vector field      261
Flow time-dependent      262
Fock space      173 209
Fock space, fermion      216
Foliation      269
Foliation, reducible      269
Forward tube      255
Four-momentum      114
Fubini — Study metric      95
Fubini — Study symplectic structure      190 235 255
Function constant along P      269
Function locally constant      272
Function time-dependent      262
Galilean group      47
Galilean transformation      36
Gauge transformation      135 157
Generalized momentum      19
Generating function      62
Generating function of a canonical diffeomorphism      63
Geodesic flow      202
Graph of a 1-form      61
Group of transformations      261
H      17
Half-form      224
Half-form bundle      232
Hamilton — Jacobi condition      237
Hamilton — Jacobi equation      60 78
Hamilton — Jacobi equation complete integral      79
Hamilton — Jacobi equation time-dependent form      80
Hamilton's equation      10
Hamilton's principle      17
Hamilton's two-point characteristic function      64 81
Hamiltonian      9 17 39 140
Hamiltonian action      39
Hamiltonian action, quantized      169
Hamiltonian completely integrable      75
Hamiltonian interaction      207
Hamiltonian time-dependent      13
Hamiltonian vector field      9
Hamiltonian vector field, complex      11
Hamiltonian vector field, time-dependent      14
Hannay's angles      243
harmonic oscillator      175 181 225 243
Heisenberg group      166 174 224
Heisenberg picture      21
Helicity      115
Hermitian structure      264
Hermitian structure, compatible with $\nabla$       264
Highest wight orbit      177

1 2

О проекте