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Araki H. — Mathematical Theory of Quantum Fields

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Название: Mathematical Theory of Quantum Fields

Автор: Araki H.

Аннотация:

This introduction to the mathematical foundations of quantum field theory is based on operator algebraic methods and emphasizes the link between the mathematical formulations and related physical concepts. The book begins with a general probabilistic description of physics, encompassing both classical and quantum physics, and presents the key physical notions before introducing operator algebraic methods. Operator algebra is then used to develop the theory of special relativity, scattering theory, and sector theory.

"This slender little volume of a little over 200 pages is a miracle ... a remarkable achievement of concision and clarity. It is a lovely introduction to algebraic quantum theory. Even workers in the field can read it with profit." — Mathematical Reviews

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 248

Добавлена в каталог: 10.06.2008

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

Предметный указатель

condition      200
space      195
$\mathcal{B}(\mathcal{H})$       21
$\mathcal{P}(\mathcal{H})$       21
$\sigma$ weak topology      211
$\sigma$ -additivity      22
$\tau$ function      138 139
$\tau$ function, connected part of a $\tau$ function      139
$\tau$ function, truncated $\tau$ 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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