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| Araki H. — Mathematical Theory of Quantum Fields |
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| Предметный указатель |
 condition 200
 space 195
 21
 21
 weak topology 211
-additivity 22
 function 138 139
function, connected part of a function 139
function, truncated function 139
*(star) isomorphism 29
Absolute value 203
Additivity 100
Additivity, weak additivity 100
Adjoint (operator) 204
Algebraic viewpoint 30
Amplification 213
Analytic continuation 151
Analyticity 151
Annihilation operator 72
Anticommutation relations 184
Antilinear map 198
Antilinearity 193
Antiunitary map 197
Antiunitary operators 198
Approximate identity 33
Archaeologists’ causality 102
Associated cyclic representation 38
Asymptotic locality 116
Asymptotic state 120
Axioms for local observables 78
Behind-the-moon argument 16
Bose statistics 180
Boson 72
Bounded 197
C* algebra 28 208
C* algebra, concrete C* algebra 28
C* norm 208
Canonical anticommutation relations 73
Canonical commutation relations 73
Cauchy sequence 194
Cauchy — Schwarz inequality 25 36 193
Causal complement 59
Causal duality 163
Causally disjoint 171
Centre 212
Charge conjugate sector 180 182
Charge quantum number 169
Charge symmetric free spinor field 220
Charged scalar field 216
Classical observable 12
Closable 204
Closed future cone 59
Closed operator 205
Closed past cone 59
Closure 204
Clustering property 87
Clustering property, exponential clustering property 89
Clustering property, multiple clustering property 97
Coboundary 62
Cocycle 62
Cofinal 23
Coherent 162
Cohomology 62
Cohomology group 62
Commutant 29 212
Commutation relations 184
Compatible system 6
complete 185
Complete additivity 22
Complete, completely additive 22
Complete, completeness 194 196
Condition BF 165
Conjugate space 197
Contraction 218
Converge strongly 194
Converge weakly 25 194
Convex combination 12
Convex set 10
Countable infinite dimension 196
Counter interpretation 128
Covariance 78
Creation operator 72
Crossed product 171
Crossing symmetry 159
Cyclic 213
Cyclic representation 38
Cyclic representation space 38
Cyclic vector 34 38 213
Density matrix 24
DIMENSION 196
Dimension function 214
Dirac equation 221
Dirac field 104
Direct integral 200
Direct product topology 13
Direct sum 30 199
Direct sum representation 31
Disjoint 30 210
Domain 204
Double commutant 212
Dye’s theorem 47
Edge of the wedge theorem 155
Eigenspace 202
Eigenvalue 202
Eigenvector 202
Energy 75
Energy-momentum 77
Envelope of holomorphy 154
Equal time commutators 148
Equivalent 185 214
expectation value 7
Extended observable 7
Extension 22
Extremal point 11
Factor 212
Factor representation 210 213
Faithful 29 209
Fermi statistics 180
Fermion 72
Finite statistics 180 181
Finitely additive measure 21
Fock space 72
Fock vacuum 72
Free charged scalar field 216
Free fields 216
Function 4 202
Gauge group 184
Generating property 78
Generator 205
Gleason’s theorem 27
GNS construction 38
GNS triplet 38
Graded local commutativity 185
Graph 204
Green’s function 151
Haag — Ruelle scattering theory 113
Helicity 70
Hermitian operator 205
Hermiticity 193
Hilbert space 193
Identity 33
Identity operator 198
Identity, approximate identity 33
Implication 46
Incoming particle (state) 109
Increasing net 23
Increasing net, bounded increasing net 23
Infinite statistics 180 181
Inner product 193
Internal symmetry 188
| Intertwining map 30 210
Invariance 203
Invariant state 54
Invariant subspace 31
Irreducible representation 66
JLD representation 92
Jordan algebra 48
Jordan isomorphism 48
Jordan product 48
Klein transformations 104
Klein — Gordon equation 74
Krein — Mil’man extremal point theorem 11
Left inverse 176
Left inverse, standard left inverse 181
Light cone 58
Lightlike 58
Lightlike, negative lightlike 58
Lightlike, positive lightlike 58
linear combination 193
Linear functional 196
Linear map 197
Linear operator 204
Linear subset 198
Linearity 193
Little group 68
Local C* system 79
Local charge 187
Local commutativity 104
Local commutativity, graded local commutativity 185
Local current algebra 189
Local filter 191
Local observable 79
Local operator algebra system of fields 184
Local W* system 80
Locality 78
Localized 166
Localized endomorphism 166
Localized excitation 160
Locally realizable 188
Locally simultaneously realizable 189
Logical product 46
Logical sum 46
Lorentz group 60
Lorentz group, full Lorentz group 60
Lorentz group, orthochronous Lorentz group 60
Lorentz group, proper Lorentz group 60
Lorentz group, restricted Lorentz group 60
Lorentz invariance 156
Lorentz transformation 60
Lorentz transformation, homogeneous Lorentz transformation 60
Lorentz transformation, orthochronous Lorentz transformation 60
Lorentz transformation, proper Lorentz transformation 60
Lorentz transformation, pure Lorentz transformation 60
LSZ asymptotic condition 133
LSZ theory 133
Measurable family 200
Measured expectation value 129
Measured value 4
Minkowski space 58
Mixture 9
Modular automorphisms 215
Modular conjugation operator 215
Modular operator 215
Momentum vector 75
Monotone property 78
Negation 46
Neutral free scalar field 74
Non-degenerate 32
Norm 28 193 197 208
Norm topology 28
normal 23 202 214
Normal commutation relations 104 185
Normal representation 214
Normal state 214
Normal, orthonormal basis 195
Normal, orthonormality 196
Nuclear 191
Nuclearity condition 192
Nuclearity index 192
Observable 3
Observable, classical observable 12
Observable, extended observable 7
Observable, function of observables 4
Observable, primitive observable 4
Observable, trivial observable 5
One particle state 66
One-parameter group 205
Open future cone 59
Open past cone 59
Operator 198 199
Operator, bounded antilinear operator 198
Operator, bounded linear operator 198
Orbit 67
Orthoautomorphism 46
Orthocomplement 46
Orthocomplemented lattice 46
Orthogonal 43
Orthogonal complement 199
Outgoing particle (state) 109
Para-Bose statistics 180
Para-Fermi statistics 180
Partial isometry 214
Particle-counter observable 129
Permutation operator 174
Phase factor 62
Phase space 12
Physical topology 13
Physically contains 15
Physically equivalent 15 42
Physically includes 42
Poincare group 61
Positive operator 203
Positive semidefmiteness 195
Positivity 193 203
Pre-Hilbert space 194
Predual 214
Primary 210
Primitive observable 4
Probabilistic description 1
Probabilistic description of classical physics 12
Projection 199
Projective representation 62
Proper time 59
Property B 164
Pure state 10
Quantum field 103 105
Quantum logic 46
Quasi-equivalent 210
Quasi-locality 115
Question 20
Quotient space 195
r-function 155
Reduction 213
Reduction formula 133
Reeh — Schlieder theorem 101
Relativistic symmetry 58 103
Representation 29 209
Representation, representation of the group 62
Restriction 31 213
Retarded function 155
Retarded function, generalized retarded function 155
Riesz theorem 197
S-matrix 109
S-matrix, connected part of the S-matrix 138
S-matrix, Lorentz invaiiance of the S-matrix 156
S-matrix, S-matrix element 110
Sakai’s theorem 214
Sector 160 169
Self-adjoint 201 205
Self-adjoint, essentially self-adjoint 205
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