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Bogolubov N.N., Logunov A.A., Todorov I.T. — Introduction to Axiomatic Quantum Field Theory
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Íàçâàíèå: Introduction to Axiomatic Quantum Field TheoryÀâòîðû: Bogolubov N.N., Logunov A.A., Todorov I.T.Àííîòàöèÿ: 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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1975Êîëè÷åñòâî ñòðàíèö: 707Äîáàâëåíà â êàòàëîã: 18.04.2010Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Indecomposability (see “Functional indecomposable” “Representation decomposable”) Independence, of axioms 350 Inductive limit 27 29 32 Inelastic processes 576 Infinite-component fields 337 349 353 564—573 577—578 610-611 Infinitesimal operator (generator) 220—221 231—233(see Ingraham, R. L. 250 351 508 652 Interaction representation (picture) 548—556 561 Intermediate-state expansion 407 Interpolating field 513 517 524—525 Invariance (see “Relativistic invariance”) Invariant subgroup 210 Invariant subspace 216—217 602 Invariants, algebraic 346—347 490—492 “Poincare invariants”) Inverse, in group 209 Inversions (see “Discrete transformations”) Involution (conjugation) 288—289 569 581 584—586 Iofa, M. Z. 281 428 652 Irreducibility of coherent subspace 602 Irreducibility of fields 257 258 328—329 350 Irreducibility of representation (see “Representation irreducible”) Irreducibility of von Neumann algebra 124 126 Isometric operator (see “Linear operator isometric”) Isomorphism 68 Isomorphism, local 131—132 Isotony 596 Isotopic spin 127—128 327 405 562 Isotropy group (see “Little group”) Iverson, G. J. 150 652 Jacob, M. 242 652 Jacobi identity 222 232—233 Jacobi polynomials 158 341 Jaffe, A. M. 426 427 466 468 469 615 616 617 618 619 620 621 622 625 626 639 645 646 652 653 Jehle, H. 242 665 Johnson, K. A. 576 642 Joos, H. 158 240 241 653 Jordan form 481 Jordan, T. F. 351 653 Jost points 473—474 487—489 495 505 510—513 518 530—531 552—553 574 Jost — Lehmann — Dyson representation 332 353 Jost, R. xvii 240 332 350 351 352 353 363 464 488 513 534 574 575 577 629 651 653 654 K-mesons 151 406 517 575 2 Kabir, P. K. 499 575 630 Kadison, R. V. 596 604 607 624 649 654 Kadyshevsky, V. G. 149 654 Kaellen, G. 464 466 468 510 654 655 Kahan, T. 242 629 Kalleh — Lehmann representation 269—270 330—332 349 357 363—364 384—385 432 466 Kalleh — Lehmann representation of commutator 330—331 443 Kalleh — Lehmann representation of Green functions 359—360 429 432—435 443—444 453 455—460 466 468 Kamefuchi, S. 466 575 576 655 Kantorovich, L. V. 15 19 20 21 24 35 37 47 105 630 Kaschluhn, F. 465 656 Kastler, D. 241 352 584 594 595 596 624 625 630 641 649 656 Kato, T. 626 650 Kats, G. I. 42 105 656 Kemmer, N. 576 656 Kernel 587 Kernel theorem (see “Nuclear theorem”) Kharatyan, S. G. 240 656 Khatset, B. I. 625 637 Khoruzhy, S. S. 281 428 466 657 Kimelson, C. O. 466 657 Klein transformation 474—475 534—538 576 Klein — Gordon equation 302—305 311 420 565 Klein — Gordon equation, invariant solutions and Green functions 333—335 Klein — Gordon equation, smooth solutions 358 365—374 428 464 free”) Klein — Gordon operator 310 Klein — Gordon operator, current defined through 382 415 Klein, O. 576 657 Kolerov, G. I. 351 508 636 Korsunsky, L. M. 271 669 Kostyuchenko, A. G. 105 644 Kraus, K 625 657 Kristensen, P. 121 240 657 Lagrangian as functional of asymptotic fields 414 Lagrangian formalism 258 274 352 360 413 414 421 454—455 548 556—561 574-575 Lagrangian formalism, algebraic approach and 600 Lagrangian formalism, axiomatic approach and 1—2 7—8 612 Lagrangian formalism, matrix approach includes 450—453 (see also “Perturbation theory” “Models” “Hamiltonian”) Lanford, O. E. 625 653 657 Langerholc, J. 466 575 609 624 657 Laplace transform 91—98 106 Lassner, G. 352 658 Lebesgue measure 47 294—295 Lee, T. D. 327 499 500 517 575 658 Legendre polynomials 17 Legendre polynomials, associated 202 Lehmann, H. 332 353 381 401 464 466 467 645 654 658 659 Lepton number 352 406 Levy — Leblond, J. -M. 142 659 Lewis, J. T. 624 640 Licht, A. L. 332 350 352 575 648 659 Lie algebra 147 220—233 “Lie Lie fields 332 352 Lie group 140 213—233 Lie’s theorems 226—233 242 Lie’s theorems for representations 232—233 Light cones 74 151 “Spectral Linear functional (see “Functional linear”) Linear operator 34—43 105 Linear operator, essentially self-adjoint 37 607—609 615 625 Linear operator, function of 42—43 112 117 148 153 Linear operator, Hermitian (see “Symmetric”) Linear operator, isometric 39 Linear operator, self-adjoint 37—39 41—43 112—118 126 593 615—617 626 Linear operator, symmetric (Hermitian) 37—39 226 Linear operator, unitary 36 38—39 41 43 139—140 550 558—560 562-563 etc.”) Linear properties, of Wightman functions 271 282 292 Lions, J. L. 73 85 88 106 644 659 Lipshutz, N. R. 575 659 Little group (stability group, isotropy group) 155—156 162 Local coordinates 214—215 Local observables, Local quantities 2—5 583 591—611 “Quasilocal Local properties of generalized functions 422—428 Local properties of S-matrix 411—414 Locality (local commutativity or anticommutativity) 245 251—252 283 350—351 415-418 Locality (local commutativity or anticommutativity) in algebraic approach 597 604 606 609 Locality (local commutativity or anticommutativity) in models 617 623 Locality (local commutativity or anticommutativity) of currents 415—416 Locality (local commutativity or anticommutativity) of infinite-component field 566 Locality (local commutativity or anticommutativity) of parafields 545—547 576 Locality (local commutativity or anticommutativity), analyticity and 505—507 Locality (local commutativity or anticommutativity), cluster decomposition property and 279—281 Locality (local commutativity or anticommutativity), gauge transformation and 532 Locality (local commutativity or anticommutativity), generalized 529—530 Locality (local commutativity or anticommutativity), generalized free field and 329 Locality (local commutativity or anticommutativity), global nature 507—509 575 Locality (local commutativity or anticommutativity), ideal associated with 291—292 Locality (local commutativity or anticommutativity), transitivity of 517—518 520—521 Locality (local commutativity or anticommutativity), Wightman functions and 268 Locality (local commutativity or anticommutativity), WLC and 511—512 Locality (local commutativity or anticommutativity)in spin-statistics theorem 474—475 Localizability (see “Position operator”) localization 350 Locally compact group 143 213 Locally convex space 598 Locally finite covering 49 Locally Fock representation 618—619 Logunov, A. A. 466 616 659 Lomont, J. S. 242 659 Lopuszanski, J. T. 577 659 Lorentz covariance (see “Covariance” “Relativistic Lorentz group 129—137 226 240 Lorentz group, algebraic invariants 346—347 490—492 Lorentz group, Casimir operators 340 570 Lorentz group, charge-conjugate spinor and 179 Lorentz group, complex 137 473—474 477—486 Lorentz group, complex extension of Lie algebra 148—149 Lorentz group, components and subgroups 130—131 Lorentz group, extended (L) 129 497 Lorentz group, inhomogeneous 131 Lorentz group, orthochronous 130—131 474 483 489—490 501 Lorentz group, proper 131 (N.B.: In some places Lorentz group, pseudoscalar invariants 490—492 Lorentz group, representations 242 250—251 481—483 501-502 Lorentz group, restricted 82 130—135 140 248 473 476 480 490 Lorentz group, SL(2) 110 131—137 144—145 241 482-483 Lorentz group, two-dimensional 617 Lorentz group, vacuum and 151 (see also “SL(2)” “Poincare' Lorentz invariance (see “Relativistic invariance” “Distributions Lorentz-invariant” “Analyticity Lorentz Lorentz transformation 129—130 133—135 159 Lorentz transformation complex 477—482 487 Lorentz transformation in Fock space 200 Lorentz transformation of algebra (automorphism) 596 617—618 625 Lorentz transformation of almost local field 376—378 Lorentz transformation of smooth solution 374 Lorentz transformation of spinor field 179 Lorentz transformation of Wightman functions 264 (see also “Lorentz group”) Lorentz transformation special (see “Pure”) Lorentz transformation, into rest frame 155 159—160 184—185 201 Lorentz transformation, orthochronous 130 Lorentz transformation, proper 130 Lorentz transformation, pure (boost) 134—135 144 155 159 617 Lorentz transformation, restricted 135 LSZ approach 2—4 358—359 381—399 415—422 464-467 Lueders, G. 575 576 647 660 Lyubarskii, G. Ya 242 630 Macdonald function (see “Bessel functions”) Macfarlane, A. J. 241 660 Mack, G. 150 652 Mackey, G. W. 240 252 630 660 Majorana basis 181—183 314 529 Majorana basis and charge conjugation 182 529 Majorana field 314 535—538 Majorana representations 567—571 578 Majorana, E. 314 577 578 660 Malgrange, B. 106 660 Mandelstam variables 497 Mandelstam, S. 497 660 Mandula, J. E. 469 635 Manifold 214 494—495 Manoharan, A. C. 510 660 Markov — Kakutani theorem 598 Marshak, R. E. 8 127 405 499 500 630 Martin, A. 428 661 Martin, W. T. 495 627 Martineau, A. 427 466 661 Mass 111 149—150 152 302 362—363 405 524 Mass degeneracy (see “Mass spectrum”) Mass gap 152 270 274 276 281 351 385—386 406 432 Mass of two-particle state 200—204 Mass shell (hyperboloid) 156—157 384 411 420—421 428 603 Mass spectrum 337 349 573 600 610—611 Mass, renormalized 460 462—463 613 Massless particles, Massless fields 281 351 577 “Neutrino”) Matthews, P. T. 171 241 352 577 630 642 643 Maurin, K. 37 105 292 295 352 630 661 Maximal Abelian set (see “Complete set”) McCoy, B. M. 469 635 Measure 88—89 Measure on hyperboloid [{dp)] 157 389 Measure, finite invariant 284—285 Measurement process distributional fields and 245—248 Measurement process distributional fields and error in 594 599 Measurement process distributional fields and locality and 251 (see also “Observables”) Medvedev, B. V. xvii 3 399 401 422 429 445 460 466 467 468 628 661 662 Meiman, N. N. 428 466 662 Mejlbo, L. 121 240 657 Mesons 193 379 399 406 442 “K-mesons” “Vector Messiah, A. M. L. 526 539 544 576 648 662 Methee, P. D. 85 106 662 Metric in Hilbert space (positivity) 109 112 117 268—269 291 Metric of Lie algebra 224—225 Metric of space-time, signature 7 (see also “Scalar product”) Metric, complex Lorentz group and 477 Metric, indefinite 109 112 Michel, L. 352 663 Microcausality 69 251 359—360 401 413—416 419—421 423 430—433 438 465 Mikusinski, J. 106 630 Minkowski, P. 486 574 663 Minlos, R. A. 240 242 340 342 344 347 353 567 628 Misra, B. 607 624 648 Mixed state 591 593 Models, nontrivial 4 5 388 468—469 582 612—623 625—626 Moeller, N. H. 510 663 Momentum conjugate (canonical) 118 121 549 552 557 558 603 Momentum conjugate (canonical) of particles 199 316 322 Momentum-space matrix elements 249 Montel space (see “Perfect space”) Moussa, P. 241 242 663 Multiplicative operator 289 Multiplicative positivity (see “Functional positive in Multiplicative symmetries 352 Multipliers 60—61 73 90 91 277 Muraskin, M. 468 663 Naimark, M. A. 143 219 220 242 340 342 353 567 584 585 587 590 624 630 663 Neighborhood 22 28 212 “Topology”) Nelson, E. 608 614 625 663—664 Net 596 507 602—604 609 Neumann function (see “Bessel functions”) Neumann, J. v. (see “Von Neumann J.”) Neutral (Hermitian) field 250 252 302—310 387 413 416—417 Neutral (Hermitian) field as example (see “Scalar field”) Neutral (Hermitian) field, complex field in terms of 311 314 Neutral (Hermitian) field, spinor (see “Majorana field”) Neutrino 150 Neutron 206 (see also “Nucleons”) Newton, T. D. 141 195 241 664 Nguyen Van Hieu 242 466 631 659 Nishijima, K. 8 464 465 468 631 663 664 Noether’s theorem 146 Nonlocal fields 252 281 350—351 508 511—512 565 Nonrenormalizable theories 249 423 428 Norm 14—16 18 20—23 119 Norm in algebra 581 585—587 Norm of functional 19 20 588 Norm of operator 34—35 39 Normal (Wick-ordered) product 308 322—323 404 408 422 452 522—523 624 Normal commutation relations (see “Anomalous commutation relations”) Normal subgroup 210 211 Normed space (see “Vector space normed”) Nuclear (kernel) theorem 12 29—32 105 106 254—255 261 Nuclear operator (nuclear mapping) 31 105 Nuclear space 31—34 105 114—115 119 120 256 295 nuclear”) Nucleons 406 442 453—454 460 465 Number operator 198 308 317—318 540—542 619 0 4 Numbering system, for sections, etc 7 Nussbaum, A. E. 608 664 Observables 109 112—118 122 123 126—127 137—140 251 591 593 610 Observables, currents and 402 (see also “Measurement process” “Local Odd distributions 84—88 Oehme, R. 467 517 575 638 658 Off-mass-shell matrix elements 398—399 401 410—415 442-443 Ogievetsky, V. I. 327 664 Oksak, A. I. 240 339 347 348 349 353 572 573 578 656 664 665 Okun’, L. B. 171 241 500 631 665 One-particle states, see Single-particle states Open set 212 Operation 591—593 624 Operator, see Linear operator Order, of distribution 26 63 425 Orthogonal groups 183 210—211 477 Orzalesi, C. A. 577 665 Out-states (see “Asymptotic states”) Overlap 384—389 396—399 O’Raifeartaigh, L. 575 655 Paley, R. E. A. C. 427 631 Paralocal field 545—547 576 Parasiuk, O. S. 102 106 468 637 665 Parastatistics, Parafields 526—527 539—547 576 Parity 327 344 496—499 562
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