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| Авторизация |
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| Woodhouse N.M.J. — Geometric quantization |
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| Предметный указатель |
Hilbert action 143
Holonomy 266
Hydrogen atom 279
Ignorable coordinates 82
Induced symplectic action 101
Integral curves 262
Integrality Condition 158
Integration 260
IO(g) 45
Isotropic oscillator 243
Isotropic submanifold 13
Isotropic subspace 2
Jacobi equation 21
Jacobi identity 11
K 206
Kaehler manifold 93 234
Kaehler metric 78
Kaehler scalar 173
Kepler system 22 277
Kepler system separation 84
Killing form 43
Killing vector 114 138
Klein — Gordon equation 134 149 176 215
L 17 25 130
Lagrange multiplier 30
Lagrange's equations 17 24 25
Lagrangian 17 64 140
Lagrangian density 130
Lagrangian Grassmannian 227
Lagrangian Grassmannian positive 91 93 178
Lagrangian higher derivative 24
Lagrangian homogeneous 25
Lagrangian regular (nondegenerate) 18
Lagrangian section 71
Lagrangian submanifold 13 69
Lagrangian subspace 2 3 227
Lagrangian subspace, complex 91
Lagrangian subspace, Kaehler 91
Lagrangian subspace, nonnegative 91
Lagrangian subspace, type (r, s) 91
Lagrangian time-dependent 25 80
Legendre transformation 19 27 72
Leray cover 273
Levi — Civita connection 263
Lie algebra, abelian 45
Lie algebra, symplectic 225
Lie bracket 259
Lie bracket, time-dependent 261
Lie derivative 185 259
Line bundle 265
Line bundle, locally constant 268
Liouville form 5
LM 231
Locally Hamiltonian vector field 10
Locally Hamiltonian vector field, complex 11
Lorentz group 112
Lorentz transformation 108
Magnetic field motion in 35
Massive particle 116
Massive particle with spin 117
Massive particle with spin in curved space-time 127
Massless particle 123
Maximal torus 103
Maxwell's equations 134—136 151
Metaplectic group 224
Metaplectic representation 218 219 225
Metaplectic structure 232
Minkowski space 107 114
moment 39
Momentum angular 45 114 177 235
Momentum linear 45
Nijenhuis concomitant 77
Noether's theorem 138—146
Null flag 112
Null vector 111
O(n), U(n) 43
O(p, q), SU(p, q) 43
Open cover, contractible 266
Orthogonal group, inhomogeneous 45
Pairing 193
Pairing half-form 224
Pairing sesquilinear 274
Papapetrou equation 127
Parabolic subgroup 105
Parallel section 266
Parity 119 122
Partial connection 67 185
Particle creation 215
path integral 205
Pauli matrices 55
Pauli — Lubanski vector 115 123
Penrose transform 254
Phase function 62
Phase space 1
Phase space, extended 14 25 27
Phase space, momentum 30
Phase space, reduced 12
Phase space, velocity 16
Poincare group 114 192
Poincare group coadjoint orbits 115
Poincare lemma 260
Poisson bracket 11 14
Poisson's equation 152
Polarization 8
Polarization, admissible 92 99
Polarization, antiholomorphic 93
Polarization, compatible with a constraint 95
Polarization, complex 92
Polarization, holomorphic 93
Polarization, invariant 102
Polarization, negative Kaehler 253
Polarization, nonnegative 188
Polarization, product 96
Polarization, real 61 65 68 92 185 194
Polarization, real compact levels 251
Polarization, reduced 95
| Polarization, reducible 65
Polarization, strongly integrable 92 97
Polarized function 92
Polarized line bundle 251
Polarized section 171
Polarized twistor 193
Polynomial observable 76
Positive frequency 147—151 176 191—193 215
Potential, connection 265 267
Prequantization 156
Prequantum, bundle 162
Prequantum, operator 250
Presymplectic manifold 12
Presymplectic manifold, reducible 12
Projection 263
Pull-back 260
Pull-back of a section 265
Pull-back of a vector bundle 265
Push-forward 260
q 16
Quantum conditions 155
Rank of a group 103
Reduction 4 12
Reduction, Marsden — Weinstein 59
Refinement of an open cover 273
Relativistic quantization 190
Restriction, of a vector bundle 265
Ricci tensor 263
Riemann tensor 263
Riemannian manifold 21
Riemannian metric 82
Root 104
Rotation group 54 57 105
S(q, q', t), S(q, q',t, t') 64
S, W 62
Scalar curvature 263
Scalar field 140
Scalar field, complex 134
Scalar field, polarization 147
Scalar field, real 134
Schroedinger equation 201
Schroedinger picture 21
Schroedinger prescription 197
Section 264
Section of a foliation 269
Semi-direct product 101
Semisimple group 43
Siegel upper half-space 94
Signature invariant 227 228
SO(3) 54
Space of motions 20
Space of motions, regularized 22 279
Spatial reflection 113
Spin 107
Spinor 108
Spinor equivalent of a tensor 110
Spinor index 108
Spinor, symmetric 111
Square root of a line bundle 267
Stationary phase 203 276
Stein manifold 273
Stokes' theorem 260
Stone-von Neumann theorem 194 209
SU(2) 54
Sub-bundle 264
Symmetry 38—59
Symmetry discrete 56
Symmetry in field theory 138
Symplectic complement 2
Symplectic frame 3
Symplectic group 5 10 224
Symplectic group Lie algebra 43 219
Symplectic manifold 1
Symplectic manifold, compact 47
Symplectic manifold, elementary 56
Symplectic manifold, quantizable 162
Symplectic potential 9 62
Symplectic potential, adapted to P 71 92
Symplectic potential, invariant 41
Symplectic structure, charged 36
Symplectic submanifold 13
Symplectic subspace 2
Symplectic vector space 1
t 261
T, P 122
Tensor product of vector bundles 263
Time reversal 113 119 122
Time-dependent differential form 261
Time-dependent vector field 261
TM, T*M 258
Torus action 48
Total space 263
TQ 16
Transition function 266 272
Transport equation 237
Twistor space 125 254 279
U(k, n-k) 90
Unit section 265
Unitary group 90 106
Unitary pseudogroup 90
Vector bundle 189 263
Vector field, invariant 50
Vector field, tangent to P 269
Vector field, time-dependent 261
Wave equation 149
Wave equation, conformally invariant 137
Wave equation, massive 191
Wave function of a polarization 186
Whitehead lemmas 44
Whitney sum 263
Wick rotation 208
WKB approximation 197 236
WKB wave function 199 237
Yang — Mills equations 136—137
[f, g] 11
[x, y] 259
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