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

Current(s), V — A (weak)      500—501
Current(s), VEV of      441—442
Cutoff      468—469 613—623 625
Cyclic group (Zw)      211
Cyclic representation      581 586 588—589
Cyclic vector      605—607 (see also “Cyclicity” “Cyclic
Cyclicity, of vacuum (completeness condition)      245 253—259 283 297 323—324 350 514 599
Dashen, R. F.      402 627
Davies, E. B.      624 640
Decomposability      (see “Functional indecomposable” “Representation decomposable”)
Decomposition of unity      (see “Partition of unity”)
Degrees of freedom, finitely many      (see “Quantum mechanics”)
Delbourgo, R.      242 672
Dell’Antonio, G. — F.      353 545 546 576 604 624 640
Delta function $[\delta(x)]$       45—48 56—57 63—66 70 83—85 100-102
Delta function $[\delta(x)]$ , derivatives      59 63—64 83 435 466
Density matrix      593
Derivation, in algebra      431
Derivative      (see “Distributions differentiation”)
Diamond, Diamond property      597 603—604 616
Differential equations of fields      (see “Wave equation” “Dirac “Klein
Differential equations, Fourier-transform solution      72 75—82
Dimension, relative      590
Dirac equation      181 183—192 207—208 241 313—314 321
Dirac equation, invariant solutions and Green functions      335
Dirac equation, orthogonality and completeness relations for solutions      185—186 208 314
Dirac equation, spinor solutions      185—186 207—208 321 “Particles spinor” “Gamma
Dirac matrices      (see “Gamma matrices”)
Dirac spinor      (see “Spinors four-component”)
Dirac, P. A. M.      578 640
Direct product      242 348—349
Direct sum      35 126
Direct-integral decomposition      143 152 162—163 203—205
Discrete transformations (discrete symmetries)      163—167 176—180 183 191—192 241 319—327 405 498—499 562
Discrete transformations (discrete symmetries), gauge transformations and      352
Discrete transformations (discrete symmetries), phases      163—167 176—180 325-327 352 499 502—503 “Time “Space-time “Charge “TCP “CP
Dispersion relations      3 4 399 465—466
Distributions      (see also “Generalized functions “Tempered
Distributions of finite order      26 63 425
Distributions, addition and scalar mutltiplication      51—53
Distributions, as classes of sequences      50—54 106
Distributions, as functionals      45—50 105
Distributions, causal      100—104 106
Distributions, change of variables      54—55
Distributions, concentrated at origin      63 83—84
Distributions, convolution      (see “Convolution”)
Distributions, differentiation      54—59 76 103—104
Distributions, division      61—66 72 76—77 106
Distributions, functions as      46—47
Distributions, homogeneous      (see “Homogeneous distributions”)
Distributions, local properties      48—49 422—428 466
Distributions, Lorentz-invariant      12 82—89 103—104 106 269—271 473-497
Distributions, multiplication by functions      59—60
Distributions, multiplication by other distributions      59—61 90—91 99—104 106 383 415 453—460
Distributions, nonnegative, see Measure operator-valued      245—249
Distributions, on mass shell      420—421
Distributions, physics, role in      45—46
Distributions, renormalization and      453—460 468
Distributions, retarded      (see “Retarded and advanced distributions”)
Distributions, terminological convention      48
Distributive laws      584
Dixmier, J.      584 587 588 605 624
Domain of analyticity      (see “Analyticity primitive
Domain of holomorphy      5 09
Domain of unbounded operator      34—35 38 615
Domain, common, of fields $(\Omega)$       2 248 294—295 310
Doplicher, S.      598 599 600 625 640 641
Dotted indices      (see “Spinors indices”)
Double-valued representations      (see also “Spin-and-statistics theorem” “Spinors” “Poincare “Representations ray”)
Drell, S. D.      2 8 460 468 627
Dual matrix $(^{t}A^{-1})$       168—169
Dual space      (see “Conjugate space”)
Duality      604
Duffin — Kemmer algebra      542—544 576
Duffin, R. J.      576 641
Dunford, N.      20 105 598 628
Dyson product      (see “Time-ordered product”)
Dyson, F. J.      332 353 467 468 575 641
Ecker, G.      150 641
Edwards, C. M.      624 641
Efimov, G. V.      466 641 332 352 641
Ehrenpreis, L.      106 642
Eisenhart, L. P.      242 628
Electrodynamics (electromagnetic interaction)      (see “Quantum electrodynamics”)
Electron      206 316
Elliptic equations      469
Energy      122 184
Energy, positivity      (see “Spectral condition”)
Energy, sign of $(\varepsilon)$       148—150
Envelope of holomorphy      509—5 10
Epstein, H.      106 415 446 467 522 573 574 575 610 625 639 642
Equal-time commutation relations      (see “Canonical commutation relations”)
Equivalence relation (equivalence classes)      125 294—295 519
Equivalence, of representations      216 558—561 581
Error, in measurements      594 599
Essential self-adjointness      (see “Linear operator essentially
Estimates, in constructive theory      615 616 619
Euclidean group (Euclidean motions, $E_{3}$ )      211 549—551
Euclidean group (Euclidean motions, in dimension 2 $E_{2}$ )      156 162 217—218
Even distributions $(\mathcal{D}+)$       84—88
Even invariant function      (see $D^{(1)}(x)$ )
Even-odd rule      537
Ex (asymptotic notation)      366
expectation value      109 113—114 116 138 591 593
Extension, of operator      35 38
External field      242 352
Extremal functional      (see “Functional indecomposable” “States extremal
Extreme points      282
E_{3}      (see “Euclidean group”)
f group      210 211
Fabri, E.      562 577 642
Factor group      211
Factor space      295 588—589
Factor, in algebra      581 589—590 604
Factor, in algebra,      607 624
Fainberg, V. Ya      281 428 466 468 642 652
Faithful representation      587 594—595 597
Fast decrease, sequences of      (see “\mathcal{S}”)
Federbush, P. G.      576 642
Feinberg, G.      150 352 642
Feldman, G.      464 577 642 643 679
Fell, J. M. G.      595 643
Fermi operator      274
Fermions, Fermi — Dirac statistics      252 281 318 402—403 526 571—573 610
Fermions, Fermi — Dirac statistics, gauge transformation and      405—406 (see also “Particles spinor” “Spinor
Feynman diagrams      103 274 454—455 459—460 466
Field equation      (see “Wave equation” “Klein “Dirac
Field operators (fields)      245—249
Field operators (fields), algebra of      (see “Algebra of
Field operators (fields), defined at fixed time      258 364—365 548—561 603 616-617
Field operators (fields), defined at point      245 282—286 35
Field operators (fields), homogeneous distribution formalism      343—345
Field operators (fields), index convention      253—254 262
Field operators (fields), products, polynomials      253—256 260 296
Field operators (fields), self-adjointness      252 607—609 616—617 625 “Heisenberg
Fierz, M.      241 576 643
Filippov, A. T.      499 634
Fock basis      119
Fock space, Fock representation      118—121 162—163 193—208 242 303 560 612—615 618
Fock space, Fock representation for infinite-component field      569—570 572
Fock space, Fock representation for parafield      539—544
Fock, V.      193 242 643
Forces, range of      281 385—386
Four-momentum      (see also “Poincare group” “Lie “Spectral
Four-point functions      270—271 360 429 435—449 562
Four-vector, Hermitian matrix and      110 132—137 notation”)
Fourier transforms      11 12 67—89 106 269 523
Fourier transforms of derivatives      72
Fourier transforms of free fields      304 313—314
Fourier transforms of generalized free field      332

Fourier transforms of Hermite function      121
Fourier transforms of Hermitian field      387
Fourier transforms of quasilocal distribution      435
Fourier transforms of retarded and advanced 4—point functions      438—441
Fourier transforms of retarded distributions      90—99 267—268
Fourier transforms of TVEV      274
Fourier transforms of Wightman functions      265—268
Fourier transforms, in $\Omega_{0}$       20 289
Fourier transforms, local properties and      424—428
Fourier transforms, sign convention      67—69 265—266 289 367
Frank, W. M.      469 643
Free fields, references      352 (see also “Scalar field free” “Spinor free” “Generalized
Freshet space      22
Fried, H. M.      468 643
Friedrichs, K. O.      352 626 628
Frobenius, F. G.      209
Froissart, M.      576 643
Full reducibility      (see “Representation decomposable”)
Function analytic      (see Analyticity)
Function of operator      (see “Linear operator function
Function, test      (see “\mathcal{S}”)
Functional (variational) derivative      359—360 401 407—412 416 430—431 444 465
Functional analysis      1 11—44
Functional(s) analytic      466
Functional(s) analytic, bilinear (bilinear form)      29—30 36 616—617
Functional(s), Hermitian      290 598
Functional(s), indecomposable      282 292—294 297—301 588 591 593
Functional(s), linear      18—21 25—26 34
Functional(s), normalized      292 598
Functional(s), positive, in $\mathcal{C}^{*}$       20
Functional(s), positive, in algebra $(\alpha^{*}_{+})$       290—291 587-589 591—594
Functional(s), S-operator as      403—404 409—414 430-432
Functional(s), space of $(\alpha^{*})$       592
Functional(s), subordinate      301
Fundamental (Cauchy) sequence      15 22 50—54 294
Fundamental solution      304—305 (see also “Green functions”)
Gachok, V. P.      577 608 625 644
Galilei group      142
Galindo, A.      539 576 644
Galois, E.      209
Gamma matrices ( $\gamma$ -matrices)      170—176 241
Gamma matrices ( $\gamma$ -matrices), groups of similarity transformations      183
Gamma matrices ( $\gamma$ -matrices), positive-energy solutions and      181
Gamma matrices ( $\gamma$ -matrices), products      172—174 499—500
Gamma matrices ( $\gamma$ -matrices), realizations      176 180—183 321—322
Gamma matrices ( $\gamma$ -matrices), two-dimensional      620—621 (see also “Bilinear invariant forms” “Spinors four-component” “Dirac
Gauge, Gauge transformation      311 352 404—406 423 532 600—601
Gel’fand — Naimark classification      338—342
Gel’fand — Naimark — Segal (GNS) construction      581 587—589 594 598 618
Gel’fand, I. M.      22 24 25 27 29 31 32 42 48 49 63 70 73 105 106 240 242 252 269 338 339 340 342 344 347 353 466 567 577 628 629 644 645
General linear group      131
Generalized eigenvector (generalized state)      39—42 105 109 114—118 197
Generalized eigenvector (generalized state) of momentum      39—40 157 199 307—308
Generalized eigenvector (generalized state), normalization      117 (see also “Rigged Hilbert space”)
Generalized free field      259 328—332 337 352—353 380 524
Generalized functions      48 57—58 422—428 466
Generator      (see “Infinitesimal operator” “Lie
George, C.      242 645
Giambiagi, J. J.      468 638
Girding, L.      73 85 88 106 241 252 350 577 644 677
GL(2)      131
Glazer, V.      106 415 467 574 639 645
Glazman, I. M.      37 39 105 627
Glimm, J.      614 615 616 617 618 619 621 622 625 626 645 646
Global nature of locality      507—509 575
GNS      (see “Gel’fand-Naimark-Segal construction”)
Goldberger, M. L.      8 629
Golodets, V. Ya      577 646
Gonzales Dominguez, A.      468 638
Good, R. H.      174 241 547
Gourdin, M.      575 647
Govorkov, A. B.      546 576 647
Graev, M. I.      106 339 340 353 628
Graph, Graph limit      35 622
Grawert, G.      575 647
Green functions      384 392 398 423 468 562
Green functions and      436—437
Green functions for spinor field $[S^{c}(x), ect.]$       335 455
Green functions in      392 400—401 464
Green functions in, reduction formula in      383—384 465
Green functions in, scattering theory results summarized      400—401
Green functions of Klein-Gordon equation $[D^{c}(x), D^{ret}(x), D^{adv}(x)]$       70—72 102—104 334—335 382 422 455 467
Green functions, analyticity      359—360 466—467
Green functions, causal      70—72 102—104 334—335 353 359—360 383 401—402 422 429 432—445 454—560 462-463
Green functions, four-point      360 429 435—449 466—467 562
Green functions, Kaelle'n-Lehmann representation      (see “Kallen-Lehmann representation of
Green functions, n-point      467
Green functions, retarded and advanced      334—335 382 401 430—434 437—441 443—445 446—449 464 466-467
Green functions, smeared      394 400—401
Green functions, time-ordered      (see “Causal”)
Green functions, unphysical singularities in      466
Green, H. S.      540 576 647
Greenberg, O. W.      328 332 352 353 526 539 544 545 546 575 576 577
Green’s ansatz      541—546
Grodsky, I. T.      349 648
Grossmann, A.      240 648
Grothendieck, A.      32 105 629
Group      209—219 242 “Poincare etc.”)
Group extensions      352
Guenin, M.      584 607 624 625 648
Guersey, F.      242 649
Guillot, J. C.      241 649
Gupta — Bleuler formulation      109 112
Haag — Araki field      609—610
Haag — Kastler axioms      581 582 596—597 599 602 603 603 618
Haag — Ruelle theory      357—358 362—380 385 388 399 464
Haag, R.      3 4 127 258 259 350 351
Haag-Araki-Kastler approach      (see “Algebraic approach”)
Haag’s theorem      475 548—562 576—577 612-614
Hadrons      151 406 “Proton etc.”)
Hagedorn, R.      240 650
Hahn — Banach theorem      21
Hall — Wightman theorem      151 434 474 489—497
Hall, D.      481 489 492 552 574 576
Hamermesh, M.      219 242 526 629
Hamiltonian, Hamiltonian formulation      8 475 548—549 556 561 576 597 612—616 620—622 626
Hankel function      (see “Bessel functions”)
Harish — Chandra      242 650
Hausdorff space      212
Heisenberg current      (see “Current” “Heisenberg
Heisenberg field      3—4 362 382 401 415 422 465 614—617 622—623
Heisenberg picture      3 137—138
Heisenberg, W.      2 362 401 465 650
Heisenberg’s nonlinear theory      112
Helicity      150 (see also “Spin” “Massless
Henley, E. M., xviii      8 629
Hepp, K.      106 281 351 363 374 383 395 397 399 464 465 468 490 492 574 626 634 650 651 654
Hermite functions      24 120—121 558
Hermitian conjugate      (see “Adjoint”)
Hermitian element, of algebra      (see “Self-adjoint element”)
Hermitian field      (see “Neutral field” “Majorana
Hermitian operator      (see “Linear operator symmetric
Hilbert problem, fifth      214—215
Hilbert space      15—17 19 30 33—44 105 112—114 122—126 240
Hilbert space in algebraic approach      593—596 599—600 602-607 “States”)
Hilgevoord, J.      465 629
Hoeegh — Krohn, R.      625 651
Hoermander, L.      106 652
Holomorphic function      (see “Analyticity”)
Holomorphy envelope, Holomorphy domain      509—510
Homogeneous distributions      338—349 502 564—565
Homomorphism      135 136
Homotopy      624
Hyperbolic rotation      (see “Lorentz transformation pure”)
Hyperboloid      (see “Mass shell” “Measure on
Hypermaximal symmetric operator      37 (see also “Linear operator self-adjoint”)
Hyperons      406
Ideal      223 290—293 296 310 587
Ideal, right, left      290—291 588
In-states      (see “Asymptotic states”)

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