Bogolubov N.N., Logunov A.A., Todorov I.T. — Introduction to Axiomatic Quantum Field Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Bogolubov N.N., Logunov A.A., Todorov I.T. — Introduction to Axiomatic Quantum Field Theory

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Название: Introduction to Axiomatic Quantum Field Theory

Авторы: Bogolubov N.N., Logunov A.A., Todorov I.T.

Аннотация:

At the end of 1960 we made plans to write a monograph about the general principles of quantum field theory and their experimental implications. We intended primarily to give an account of the progress of the theory of dispersion relations since the appearance of the book of Bogolubov, Medvedev and Polivanov ([BMP]. As an introduction we wanted to include a review of the various approaches to axiomatic field theory. This introduction had to cover not only the formulation of Bogolubov, Medvedev and Polivanov, based on the apparatus of functional derivatives of the 5-matrix and the condition of microcausality, but also the field formulation associated with the names of Wightman, Haag, Lehmann, Symanzik, Zimmermann, and others. In the course of the work the tasks (and with them the size) of the introduction grew larger and larger, until eventually it developed into this book.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1975

Количество страниц: 707

Добавлена в каталог: 18.04.2010

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Предметный указатель

$D^{(1)}(x)$ (even invariant function)      334—335 511 528
$d_{\chi}$       (see “Homogeneous distributions”)
$P(\Phi)$ models      620 625—626
$SL(2)\otimes SL(2)$       137 478—481 533
$SL(2, \mathbb{R})$       156
$Sp(2, \mathbb{R}), Sp(4, \mathbb{R})$       568—569
$S^{*}_{V^{+}}$       91 95
$S_{\infty}$       426—427
$\alpha *$ (dual of Hermitian elements of $\alpha$ )      598
$\alpha$       (see “Quasilocal observables” “Algebra of
$\alpha^{+}(O)$       (see “Algebra of
$\alpha^{H} *$       (see “Functionals positive”)
$\mathcal{D}$       22—25 27—28 32 48 69 105
$\mathcal{D}^{*}$ (spaces of distributions)      27 48 55 69 85 105
$\mathfrak{L}_{2}$ (space of square-integrable functions)      16 30 38—40
$\omega$       (see “Domain common”)
$\Omega_{0}$ (space of finite test-function sequences) $\Omega_{0}^{*}$       287—296 310
$\Omega_{1}$ (nuclear space generated by fields)      256
$\Phi^{4}$ interaction, in Yukawa theory      455 04
$\Phi^{4}$ model      468—469 582 612—620 625- 626
$\textit{1}$ (space of sequences of fast decrease)      32 43—44
$\textit{1}$ (space of sequences of fast decrease), f-fold sequences $(\textit{S}_{f})$       119—121 197—199 303
$\textit{c}$ (spaces of differentiable functions)      17—18 20—22 25
Abelian (commutative) group      209
Abelian algebra      223 597 607
Absolutely continuous function      37
Acharya, R.      575 632 633
Additive operator      139 239
Adjoint (Hermitian conjugate)      36—37 569 586
Adjoint (Hermitian conjugate) in algebra      (see “Involution”)
Adjoint (Hermitian conjugate) of field operator      253 260 262 529 531—532 538
Adjoint representation      224
Adler, S. L.      402 627
Admissible observable      115 116
Advanced distribution      (see “Retarded and advanced distributions”)
Advanced product $(A_{\chi})$       392—399
Affinors      174
Akhiezer, N. I.      37 39 105 627
Akilov, G. P.      15 19 20 21 24 35 37 47 105 630
Aks, S.      0 575 655
Algebra      95 256 584
Algebra of bounded operators $[\beta(H)]$       586 589
Algebra of fields $(\alpha, \mathfrak{F})$       255—257 297—300 599-601 602 609 610 614 616 624 625
Algebra of open set $[\alpha(O), \mathcal{R}(O) ]$       257—258 350 581 596—597 599-610
Algebra of quasilocal observables $(\alpha)$       596—599
Algebra of unbounded operators      624
Algebra, normed      301 584—585
Algebra, nuclear      287—289 301
Algebraic approach      4 525 573 577 581—611 624—625
Algebraic approach, field theory and      582 583 590 597 607—611
Algebraic approach, scattering theory in      610—611
Almost local field      351 357 364—366 374—378 384-390
Analytic completion      429
Analytic continuation      332 445—446
Analytic extension      509
Analytic vector      608
Analyticity causality and      432—433 476
Analyticity in manifold      493—495
Analyticity in several variables      467
Analyticity of Fourier transform of retarded function      91—98 267—268 432—434 473 476
Analyticity of Green functions      359—360 429—449 454460 473 476
Analyticity of Lie group coordinates      214—215
Analyticity of Wightman functions      267—268 473 476 487 504—510
Analyticity on open real set      605—606
Analyticity, Lorentz invariance and      434 473—497 574
Analyticity, primitive domain of      429 438—441 447—449
Angular momentum of two-particle state      200—204 (see also “Spin” “Poincare “Lie
Angular momentum,      147 156 175 205 596 “Poincare “Lie
Angular momentum, complex      227 (see also “Spin” “Poincare “Lie
Angular momentum, orbital      189 516 “Poincare “Lie
Anomalous commutation relations      474—475
Anticommutation relations canonical      566 572 577
Anticommutation relations of $\gamma$ -matrices      171
Anticommutation relations of field with creation-annihilation operators      403 410
Anticommutation relations of nonlocal scalar field      511—512
Anticommutation relations, discrete transformations and      322
Antiparticles      205—208 322 515 517
Antisymmetric unit tensor $(\epsilon_{jkl}, \epsilon_{\mu\nu\lambda\sigma})$       133—134 146—147
Antiunitary operator      110 139 140 164—165 167 241 298 322 515
Antoine, J. — P.      240 633
Araki, H.      281 351 466 523 545 573 575 576 604 610 624 625 633 634
Arbuzov, B. A.      499 634
Artin, A.      241 627
Associative algebra      584
Asymptotic completeness      358 378—380
Asymptotic completeness,      406 523
Asymptotic conditions      3 357—358 362—363 365—367 381—384 389-390 465
Asymptotic fields      358 359 366—368 381—382 422 430—432 465 549
Asymptotic fields, relative weak locality and      5 20
Asymptotic fields, TCP transformation of      514—515
Asymptotic states      358 365—368 385—386 402—407 515-517
Asymptotically abelian algebra      625
Automorphism(s)      136 139—140 210 596
Automorphism(s), inner, outer      136
Automorphism(s), space-time, in $\Phi^{4}$ model      616—618 625
Axial vector      146 154 344 500—501
Axiomatic approach      1—5 362—363 460 612 “BMP “LSZ “Algebraic
Axioms, enumerated      117—118 142 151 152 248—252 256 379
B* -algebra      585 (see also “C*-algebra”)
Banach algebra (Banach ring)      584—585
Banach space      15
Bardakci, K.      466 575 634
Bargmann — Hall — Wightman theorem      473—477 481—486 513 518 533 548 574
Bargmann, V.      574
Bargmann’s proof, of Wigner’s theorem      234—239 242
Bargmann’s theorem      141—142
Barton, G.      464 627
Baryon number      122 153 206 352 379 406 600
Baryons      151 406 “Proton”).
Baumann, K.      351 465 635 669
Belinfante, F. J.      241 635
Bender, C. M.      469 635
Berezansky, Yu. M.      105 608 625 627 635
Berezin, F. A.      577 627 635
Bessel functions      70 81 335 370
Bialynicki — Birula, I.      540 636
Bibliographical conventions      6 632—633
Bicompactness      213
Bilenky, S. M.      575 636
Bilinear form      (see “Functional bilinear” “Scalar
Bilinear invariant forms of Dirac equation      178 322—323 499—501
Bilinear invariant forms of Majorana representations      567—568
Bispinor      (see “Spinor four-component”)
Bjorken, J. D.      2 8 460 468 627
Blokhintsev, D. I.      351 508 636
BMP approach      3 400—422 430—432 450—453 465—468 525
Bochner — Schwartz theorem      269 271
Bochner, S.      495 627
Bogolubov transformation      (see “Canonical transformation”)
Bogolubov, N. N.      xvii xviii 3 8 72 102 106 146 171 186 241 242 322 333 336 352 399 401 405 409 414 422 429 445 455 465 466 467 468 556 561 574 577 625 628 636 637
Bohm, A.      240 637
Bohr, N.      350 637
Bollini, C.      468 638
Boost      (see “Lorentz transformation pure”)
Borchers classes      474 517—525 575 583 604 609
Borchers classes and      519—520 (see also “Irreducibility of
Borchers — Zimmermann criterion      603 607—608
Borchers, H. J.      257 259 292 297 300 350 351 352 517 575 606 607 625 638
Born term      463
Bose operator      274
Bosons, Bose — Einstein statistics      194 252 402—403 526 564 572
Bound states      465
Boundedness of linear functional      18—19
Boundedness of operator      34—35 116
Boyce, J. F.      242 672
Bremermann, H. J.      467 638
Brenig, W.      363 464 639
Broken symmetry      475 562—563 577
Bros, J.      106 415 467 574 639
Bruhat, F.      252 639

Burgoyne, N.      576 639
C*-algebra      4 581—611 614 616 624—625
C-convex envelope      508
Cannon, J. T.      617 625 639
Canonical basis, in $d_{\chi}$       340—343 564 570
Canonical commutation relations for infinite-component field      566 (see also “Anticommutation relations” “Commutator”)
Canonical commutation relations for position and momentum      118 195 “Commutator”)
Canonical commutation relations for scalar field      305 311 465 557—561 “Commutator”)
Canonical commutation relations in $\Phi^{4}$ model      617 (see also “Anticommutation relations” “Commutator”)
Canonical commutation relations in discrete basis      558—560 (see also “Anticommutation relations” “Commutator”)
Canonical commutation relations inequivalent representations      548 556—561 577 “Commutator”)
Canonical commutation relations of creation-annihilation operators      304—305 (see also “Anticommutation relations” “Commutator”)
Canonical commutation relations, singular      561 (see also “Anticommutation relations” “Commutator”)
Canonical commutation relations, strange representations      475 560—561 “Commutator”)
Canonical commutation relations, Weyl form      559 569 “Commutator”)
Canonical coordinates      220 227—232
Canonical formalism      (see “Lagrangian formalism” “Hamiltonian” “Canonical
Canonical transformation, linear      559—560
Cantor, G.      50 294
Cartan, E.      225
Cartan, E. J.      241 628
Cartesian product      30
Casimir operators      225 (see also “Poincare' group invariants” “Lorentz “Casimir
Cauchy inequality      588
Cauchy principal value      5
Cauchy sequence      (see “Fundamental sequence”)
Causal distribution      (“Distributions causal” “Green causal”)
Causal envelope      597 603—604
Causal Green function      (see “Green functions causal”)
Causal shadow      597
Causality      2 247 414 465
Causality in algebraic approach      597
Causality, analyticity and      432—433 476
Causality, primitive      258—259 597 “Microcausality”)
Cayley parametrization      479—480
Center of algebra      589
Center-of-mass frame      (see “Lorentz transformation into
Characteristic subgroup      210
Charge conjugation      131 179—180 183 192 206 320—323 325—326 352 529 568
Charge conjugation in homogeneous distribution formalism      344—345
Charge conjugation, space reflection and      325—326
Charge renormalization      613
Charge, electric      122 153 206—207 250 311—318 596 599 600
Charged field      (see “Complex field”)
Chen, T. W.      460 468 639
Chernikov, N. A.      576 639
Chou Kuang — Chao      242 327 640 664
Circumflex, denoting omission      408
Classical theory, algebra of      597
Clifford algebras      241 499 “Anticommutation
Closed graph theorem      35
Closed operator      35
Closed subspace      216—217
Closure, of operator      37
Cluster decomposition property      151 272—282 293 351 531 576
Coherent subspace (Superselection sector)      123—127 139 142 250—251 312 602 605 607 609
Coherent subspace (Superselection sector), discrete transformations and      326—327 (see also “Superselection rule”)
Commutant      299—300 589 601—605
Commutation relations      (see “Commutator” “Anticommutation “Canonical “Anomalous “Spin-and-statistics
Commutator in group      221
Commutator in Lie algebra      221—222
Commutator in parafield theory      540—546
Commutator Kaellen — Lehmann representation      330—331
Commutator of current with field      417—418
Commutator of field with creation-annihilation operators      403
Commutator of free scalar field [D(x)]      302—303 328 333—335 382 418 554—556
Commutator of functional differentiations      409
Commutator of generalized free field      328—331
Commutator of Heisenberg and asymptotic fields      465
Commutator of S-operator with creation-annihilation operators      409—412
Commutator of vector field      561 (see also “Canonical commutation relations” “Anticommutation
Compact energy, vector of      605—606 617
Compact group      143 213 219 225—226 600
Compact support, functions of      (see “\mathcal{D}”)
Compactness      213
Compactness, Haag — Swieca      573
Compactness, relative      24
Compactness, weak      618
Compatible norms      21—22
Compatible topologies      27
Complement, of invariant subspace      217
Complete set, of operators      152—153 451—452
Complete space      15
Completeness, of field theory      (see “Cyclicity”)
Completion, in norm      25 33
Complex (charged) field      250 283—284 311—314 610
Complex conjugation, antiunitary operators and      164
Composite models      379
Cone      74 151 440 488 494
Cone of positive functionals $(\alpha^{*}_{+})$       592 594
Cone, double      606
Conjugate space      19—21 26—29 105 598
Conjugate, of spinor (Dirac conjugate)      178 183 186
Conjugation      (see “Involution”)
Connectedness      213
Connectedness, simply      135 213
Constructive field theory      (see “Models”)
Continuity      212
Continuity of functional      18—19 25
Continuity of operator in nuclear space      119—120
Continuity of representation      216—219
Continuity, absolute      37
Continuity, weak, of field      249
Continuity, weak, of representation      216
Continuous group      (see “Topological group”)
Continuous spin      150
Convergence      212
Convergence in $\mathcal{S}$ and $\mathcal{S}^{*}$       23 29
Convergence in $\Omega_{0}$       287—288
Convergence in $\Omega_{1}$       21 25 6
Convergence in C*-algebra      585—586
Convergence in conjugate of countably normed space      28—29
Convergence in countably normed space      22
Convergence in norm (uniform)      17 585—587
Convergence in normed space      15 17
Convergence in nuclear space      32
Convergence, strong      15 28 32 586 587 615
Convergence, weak      28 32 216 381 586 598 616
Convex set      282
Convolutes $(\Theta_{C^{'})$       73—74 375
Convolution      72—76 95 104 456—459
Convolution multiplication and      73 93 99—100
Coordinates, generalized      118
Coulomb law      281
Countably normed space      (see “Vector space countably
Coupling constant      450—451 455 469 614
Covariance in algebraic approach      596 609
Covariance of analytic functions      473—497 574
Covariance of fields      249—251 (see also “Relativistic invariance” “SL(2) representations”)
Covering group      135
Covering, by open sets      49 213
CP transformation, CP violation      498—499 501 “Parity”)
Creation and annihilation operators      118—121 304—308 312 315—318 320—321 336 404 577 613
Creation and annihilation operators for parafield      539—544
Creation and annihilation operators in x-space      309 619
Creation and annihilation operators, asymptotic      389—390 403
Creation and annihilation operators, commutation relations with fields and S-operator      403 409—410
Creation and annihilation operators, majorana representations and      568—570 578
Creation and annihilation operators, normal commutation relations, derived      528
Creation and annihilation operators, notation      389
Current(s)      401—402 413—419 421 441—445 577
Current(s) as derivative of S-operator      3 359 401 413 415 430—432
Current(s) in Borchers class of field      521—522
Current(s) in Yang — Feldman equations      358 382 415 417
Current(s), algebras of      402
Current(s), electric      322—323 382 413
Current(s), Kaellen — Lehmann representation      432
Current(s), reconstruction theorem for      466
Current(s), satisfy axioms      432 514
Current(s), TCP transformation of      514

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