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| Авторизация |
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| Thaller B. — The Dirac equation |
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| Предметный указатель |
Absolutely continuous spectrum 130
Abstract Dirac operator 139
Abstract Dirac operator, c-dependence 177
Abstract Dirac operator, self-adjointness 145
Acausality 28
Active transformation 45 57 304
Adiabatic switching 299
Aharanov — Casher theorem 198
Aharonov — Bohm effect 312 315
AKNS-ZS evolution equations 316
Analytic perturbation theory 183
Angular momentum, orbital 8
Angular momentum, spectrum 126
Angular momentum, spin 8
Annihilation operator 277
Anomalous moment 182 305
Anomalous moment, electric 111 123 152
Anomalous moment, magnetic 110 123 147 153 218 309
Anti-unitary operator 51 102 104
Antiparticle 14 275
Asymptotic completeness 224
Asymptotic completeness, Coulomb 241
Asymptotic completeness, magnetic fields 247
Asymptotic completeness, short-range 239
Asymptotic configurations 224
asymptotic freedom 224
Asymptotic observable 315
Atiyah — Singer index theorem 310
axial anomaly 166 319
Biedenharn transformation 314
BJL operator 214 217 220 314
Bogoliubov transformation 287
Bohr-magneton 110
Boost 45 70 74
Born's statistical interpretation 5
Bound state 131 189 218 223 268 272 275
Breit — Fermi Hamiltonian 312
Callias index formula 174
Canonical anticommutation relations 278
Carleman inequalities 308
Cauchy problem 5
Cauchy — Riemann equations 197 198
Cayley transform 157
Center of energy 8 49 57
CHARACTER 84
Characteristic function 5
Charge conjugation 14 36 275
Charge conservation 298
Charge operator 283
Charge quantization 313
Charge sector 284
Chiral transformation 319
Chirality 41
Cini — Touschek transformation 156 310
Classical limit 308
Classical velocity 19 227
Classically allowed region 34 131
Classically forbidden region 34
Closure of an operator 142
Cohomology 64 65
Collapse to the center 306
Commutation methods 308
Compact operator 229
Continuous spectral subspace 223
Coset 82
Coulomb gauge 245
Coulomb potential 114 130 136 148 208 240 306 309 314 315
Coulomb singularity 218
Coupling constant 114
Covariant Dirac equation 97
Covariant states 94
Covariant states-scalar product 96
Covering group 59 62
Covering group, Lorentz group 69 76
Covering group, Poincare group 60 76 99
Covering homomorphism 73
Creation operator 277
Cylindrical symmetry 206
Darwin term 190
Decay at infinity 116
Defining representation 93
Determinant 170
Dilation generator 227
Dirac equation 3
Dirac equation invariance 100
Dirac equation, covariant form 97
Dirac equation, one-dimensional 120
Dirac equation, Poincare transformation 108
Dirac matrices 2 73 77
Dirac operator 7 107
Dirac operator with supersymmetry 149 209
Dirac operator, abstract 139
Dirac operator, nonrelativistic limit 179
Dirac operator, partial wave decomposition 128
Dirac operator, resolvent 179
Dirac operator, second quantization 283
Dirac operator, self-adjointness 112
Dirac operator, spectral theory 129 131 308
Dirac sea 279 302
Dirac — Pauli representation 36
Discrete transformations 46 102
Double well 308
Dual action 85
Dual group 84
Einstein causality 30
Electric potential 109
Electromagnetic field tensor 110
Electromagnetic potentials 109
Embedded eigenvalues 130 135
Energy operator 5
Energy-momentum relation 2
Essential spectrum 114 202
Even operator 139
Even parity spinors 88
Event 43
Evolution kernel 15 38
Evolution operator 5 251
Exited states 211
expectation value 6 21
External field 107 275
External field problem 317
Factor set 82 86
Factorization 308 314
Fermion-vortex system 311
Feynman propagator 39
Field, electromagnetic 109 110
Field, operator 280
Field, pseudoscalar 111
Field, pseudovector 111
Field, scalar 108
First-order correction 188
Fock space 276
Foldy — Wouthuysen representation 25
Foldy — Wouthuysen transformation 11 102 154 196 209 302 305 309
Fourier transformation 9
Fractional charge 319
Fredholm determinant 171 264 310
Fredholm index 158 294 316
Fredholm operator 158
Free Dirac operator 7 9
Gamma matrices 72
Gamma matrices commutators 79
Gamma matrices products 79
Gamma matrices standard representation 77
Gamma matrices traces 80
Garding domain 55
Gauge invariance 119
Gauge transformation 119
Grading operator 139
Ground state 210
| Haar measure 55 82
Hamilton function 241
Hamiltonian 5
Hamiltonian with supersymmetry 140 156
Hardy's inequality 112 149
Helicity operator 40
Hilbert-Schmidt condition 249
Hodge dual 110
Hole theory 279 302
Hopf tori 200
Hyperbolic sine-Gordon equation 316
INDEX 158 200 264
Index topological invariance 167
Index, Callias formula 174
Index, heat kernel regularization 160
Index, resolvent regularization 160
Index, Witten index 165
Induced representation 83 305
Induced representation, irreducibility 92
Inertial frame 43
Infinitesimal generators 48 100
Inner automorphism 85
Instantaneous spreading 30
Instanton 311
Intertwining relations 225
Invariance of the Dirac equation 100
Invariance of the domain 20
Invariance of the essential spectrum 114
Invariance principle 242
Invariant domain 21 228 303 304
Invariant measure 88
Inverse scattering 267 317
Involution 139
Irreducible 53
Isotropy group 86
Jost solution 220 261
Kato — Rellich theorem 61 112 251
KdV equation 255
Kinetic energy correction 190
Klein — Gordon equation 2 38 153 302
Klein's operator 139
Klein's paradox 120 131 307
Konrady's trick 61
Korteweg — de Vries equation 255
Krein's spectral shift 161 226 310
Kronecker symbol 3
Laplace operator 2
Lax pair 256
Left action 82
Level crossing 219
Level order 314
Lie algebra of the Poincare group 48
Lie bracket 49
Lifting 53 63
Limiting absorption principle 308
Little group 87 88
Local compactness 115 223
localization 26 28 303
Long-range potential 240
Lorentz covering group 69 76
Lorentz group 44
Lorentz metric 43
Lorentz transformation 44 304
Mackey decomposition theorem 89
Mackey states 83
Magnetic field 113 119 142 152 174 190 194 244 310 312
Magnetic monopole 123 307 312 314
Majorana representation 36
Mass shell 46 91
Matrix trace 160
Minimal coupling 109 177 302
Minkowsky space 43
Miura transformation 253
MKdV equation 316
Modified Korteweg — deVries equation 255
Modified time evolution 240 244
Modified wave operators 241
Moller wave operators 224
Momentum operator 8
Momentum space 9
monopole 312
Monopole harmonics 313
Negative energies 14 120 283
Negative energy subspace 10
Nelson's theorem 58 304
Nelson's trick 143 151
Neutrinos 4
Neutron 153
Newton Wigner operator 25 303
Non-stationary phase 33 245
Nonrelativistic limit 179
Nonrelativistic limit, eigenvalues 188
Normal ordering 285 300
Number of eigenvalues 136
Number operator 283
Observable 4
Observable, Foldy — Wouthuysen representation 25
Observable, restricted 24
Odd operator 139
Odd parity spinors 88
On-shell scattering operator 226
One-particle operator 284
One-particle subspace 275
Operator valued distributions 318
Operator, closure 142
Operator, even/odd part 139
Operator, Fredholm 158
Operator, trace class 159
Orbit 86
Orbital angular momentum 8
Orthogonal projection 5
Overcritical field 299
Paramagnetic inequality 313
Parity 93 104 111
Parity transform 46
Partial wave subspace 128
Passive interpretation 304
path integral 303
Pauli exclusion principle 278
Pauli lemma 74
Pauli matrices 3 49 68
Pauli operator 152 195
Pauli — Runge — Lenz vector 215
Periodic point interaction 306
Perturbation determinant 171
Phase shift 220
Phase shift operator 226
Plane-wave solutions 40 261
Poincare group 47
Poincare group, covering group 76
Poincare group, Lie algebra 49 56
Poincare group, orbits 87
Poincare transformation 47 99
Point interaction 306
Polar coordinate 123
Polar decomposition 69 143
Position operator 26 303
Position probability density 8 32
Positive energy subspace 10
Potential Poincare transformation 108
potential step 121
Potential, Coulomb 114
Potential, electric 134
Potential, electromagnetic 109
Potential, local singularities 112 120
Potential, matrix 107
Potential, pseudo vector 111
Potential, pseudoscalar 111
Potential, scalar 108 134
Potential, spherically symmetric 122
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