 ’th exterior product 64
Bargmann — Fock representation 23-25 27 142-143 146 147 149 151 157 159
Blattner — Kostant — Sternberg kernel 3 12-13 15 17 22 23 24-25 26 27 77 80-81 83 107 134 137 142 147-149 156-157 196 209-210
Bohr — Sommerfeld variety 10 11 15 16 25 33 71-72 73 76 126 144 150 154 187
Bohr-Sommerfeld conditions 10 11 13 25 33 64 71 72 107 112-113 154 187
Canonical coordinate systems 5 20 41 121
Canonical momentum associated to a vector field 20 121
Canonical one-form 19 40 41
Canonical transformation 38 47
Charge superselection rules 187
Charged symplectic structure 30 42-43 168
Complete polarization 12 73
Completeness Condition 10-11 73
Complex line bundles 6 8 51-53
Connection form 53-55 181
Covariant derivative 54-55
Curvature form 55 173 181
Dirac quantization condition 30-31 169-170
Distributional wavefunctions 10 71 72 73 75-76 80-81 150
Energy representation 25-27 73 142 150 156 1577 159
Equivalence of quantizations 1-2
Evolution space, classical 6 27 28 45 48 160
Evolution space, quantum 28- 29 162-3
Feynman path integral 19 22- 23 134 139 140-141
Fundamental vector field 52
Generating function 47-48 49-50
Hamiltonian vector field 5 39 41
harmonic oscillator 24 25 27 73 146-147 149-159
Hermitian inner product 7 56 63- 64 101
Horizontal distribution 53 181
Horizontal lift 53
Horizontal vector field 53
Induced metalinear frame bundle 94
Inertial frame 27-28 29 45 48 50 160 166
Intertwining operators 1-2 3 12 15 17 25 27 34 77 108 148-149 159 188 190 192 197
Kaluza electrodynamics 32-34 180-183
Klein — Gordon equation 32 174
Lagrange bracket 5 19 28 33 34 38 40 42 46 114 120 160 183-184 198 199
Lagrangian distribution 61
Linear frame 64
Linear frame bundle 64 93
Metalinear frame 66
Metalinear frame bundle 25 64- 65 79 88 94 101 114
Metalinear group 64
Metalinear positive Lagrangian frame 92
Metalinear positive Lagrangian frame bundle 2-94 101
Metaplectic frame bundle 12 25 27 79 87-8 8 92
Metaplectic group 87
Momentum representation 23 142
Non-relativistic dynamics, classical 6 27-28 45-50
| Non-relativistic dynamics, quantum 29-30 160-167
Non-relativistic single particle 6 18-19 22 23-24 114-120 142-146
Non-relativistic spinning particle 34-37 198-213
Partial covariant differentiation 66-67
Pauli equation 37 213
Pauli representation 35-37 204-205
Phase space 5 19 27 28 30 33 38 40 42 45 46 114 120 150 160 168 180 198
Poisson algebra 1-2 5 40 57 59
Poisson bracket 1 39-40 42
Polarization 9 60 61 101
Position representation 114
Position-type functions 20 121
Positive Lagrangian frame 88 90
Positive Lagrangian frame bundle 88 89-91
Positive polarization 12 63 88
Prequantization 6-7 8 51 55 59
Prequantization condition 6-7 30 35 55 169 202
Prequantization line bundle 6 9 28 30 55-56 101
Prequantization map 6 7 51 58-59
Quantizable functions 1 3 100
Quantization 1-2 14-15 17 103-111
Quantization map 1 14-15 103-104-107 108-111
Quantization of charge 7 30- 31 73 169-170 187
Quantization of spin 7 35 202
Quasi-classical approximation 134 136-137
Real polarization 10 11 63 73 108
Relativistic charged particle 5-6 30-34 42-45 168-197
Representation space 7 9 10-12 16-17 18 21 23- 25 29 31 33-34 35-36 60 63 67 69-70 71 74- 76 101 112-113 115 126 144 145 150 156 171 173-174 187 204-205 206
Scalar product 10 18 21 23 27 31 36 63-64 69 70 73 74 76 126 144- 145 154 156 171-172 190 206
Schr dinger equation 19 21- 21-22 120 134
Schrdinger equation, time- dependent 29-30 160 163 167
Schrdinger representation 18-19 22 23 24-25 26- 77 114 122 142 147 149 157 161
Space-time, Galilean 27 46
Space-time, relativistic 30 42
Square-integrable wave functions 10 11 69-70 75 80
Strongly admissible pair of polarizations 77 82
Strongly admissible polarization 9 11 61 62-63 65 73
Superselection rules 16-17 113 187
Symplectic form 5 38 41
Symplectic frame 87
Symplectic frame bundle 12 87 89
Symplectic group 87
System of particles 19-23 50 120-134
Time-dependent dynamics 6 30 48-49 160
Transverse pairs of polarizations 13 77 117
Unitary relatedness 1-2 12 17 25 27 34 77 108 149 159 188
van Vleck determinant 19 136
Vertical distribution 53 122 181
Vertical vector field 53
WKB approximation 136
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