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

Àâòîðû: 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: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1975

Êîëè÷åñòâî ñòðàíèö: 707

Äîáàâëåíà â êàòàëîã: 18.04.2010

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Spherical harmonics      202
Spin      111 150 153—158 161 167 175 184 185 316 318 322
Spin affinors      174
Spin, discrete-transformation phase conventions and      326—327
Spin, higher      241—242 337 343—349 352 353 576
Spin, superselection rule      122 250—251
Spin, TCP and      515—516
Spin-and-statistics theorem      4 252 337 474—477 526—538 576
Spin-and-statistics theorem for parafields      545—547 576
Spin-and-statistics theorem, infinite-component counterexamples      564—566 577
Spin-and-statistics theorem, nonlocal counterexample      511—512
Spin-and-statistics theorem, TCP theorem and      513 538 572—573 574—575
Spinor field      179 250—252 264—265 281—282 319—327 402—404 527 534 620—623
Spinor field in algebraic approach      600—601
Spinor field in functional differentiation      408—409
Spinor field, charge conjugation phase convention      345
Spinor field, free      313—319
Spinor field, functions associated with [S(x), etc.]      315 318—319 322 335
Spinor field, gauge transformation      404—406
Spinor field, Lagrangian      557
Spinor field, TCP transformation      499—504
Spinor field, TVEVs and      273
Spinors      122 168—169 241 247
Spinors, discrete transformations and      169—170 176—180 182—184 187 191-192 319—327 352 501—504
Spinors, four-component (Dirac spinors, bispinors)      168—192 241 314 321 340—342 516 529
Spinors, indices (dotted, etc.)      168—169 482—483 501-504
Spinors, infinite-component      565
St${\O}$rmer, E.      577 666
Stability, of vacuum and one-particle states      368 380 407 411 432 442—443 452
Stapp, H. P.      467 671
Star algebra (*-algebra)      584—585
Star isomorphism      587
Star representation (*-representation)      569
States, State vectors      109 112—128 137—138 142 591 610
States, State vectors in algebra (Cfc* )      591—595 598
States, State vectors in free field theories      303 306—308 316
States, State vectors of generalized free field      331—332
States, State vectors, discrete transformations and      323—327
States, State vectors, extremal invariant      625
States, State vectors, mixed and pure      591
States, State vectors, physically realizable      122—128
States, State vectors, space of      112—128 242 379 618—619
Statistical mechanics      625
Statistics      526 539
Steinmann identities, Steinmann quartets      360 446—449 467
Steinmann, O.      392 446 464 466 467 651 671 672
Stieltjes integral      20 88
Stone, M. H.      609 672
Stora, R.      241 242 663
Stoyanov, D. Tz      341 342 353 577 672
Strathdee, J.      242 576 655 672
Streater, R. F.      xvii 240 327 349 350 351 374 378 445 464 467 512 534 575 577 611 619 631 648 672 682
Strocchi, F.      562 577 642
Strong interactions      2 127—128 151—152 405—406 496 562
Strong topology      (see “Convergence strong”)
Structure constants      222—226 230—233
Stueckelberg, E. C. G.      465 672 673
SU(2) (special unitary group)      134 144 155—156 213 216 224
SU(2) (special unitary group), isospin and      127—128 405
SU(2) (special unitary group), representations      156 158 340—341 550
SU(2, 2)      172
SU(N)      211
Subgroup      210
Sudarshan, E. C. G.      8 127 150 351 405 545 546 575 576 630 634 640 653 673
Sukhanov, A. D.      460 466 662 673
Summation convention      129
Superconductivity      577
Superposition principle      126
Superselection rule(s)      122—128 142 240 250—251 326 379 534 535 537 596 599 601
Superselection rule(s), charge      206—207 251 312
Superselection rule(s), noncommutative      127—128
Superselection rule(s), univalence (spin)      122 250—251 379 534
Superselection rules and      122 127—128 379
Support      23
Support of analytic functional      466
Support of distribution      49 424—428
Sushko, N. V.      577 673 679
Swieca, J. A.      259 380 573 650
Symanzik, K.      381 401 464 467 468 658 659 673
Symmetric operator      (see “Linear operator symmetric”)
Symmetries      352 577
Symmetries of physical world      131 404—405 498—499
Symmetries unitary operators and      36 242 475 562—563 577 “Relativistic “Isotopic
Symmetries, broken      475 562—563
Symmetrization operator      197
Symplectic group      568—569
T-matrix      436 496—497
T-product      (see “Time-ordered product”)
Tachyons      150
Tagamlitsky, Ya      106 673
Takahashi, Y.      576 655
Taylor series, as generalized function      425
Taylor, J. G.      467 638 576 643
TCP and spin-statistics not implied      610—611
TCP operator      298—299 322 474 498—504 511 514-519
TCP operator and      504 (see also “Lorentz group” “Relativistic
TCP operator in homogeneous distribution formalism      345 502
TCP theorem (TCP invariance)      4 337 474 476 498—504 512—518 538 574-575
TCP theorem (TCP invariance) for parafields      545—547
TCP theorem (TCP invariance), asymptotic states and      379
TCP theorem (TCP invariance), experimental verification      517 575
TCP theorem (TCP invariance), infinite-component counterexamples      567—573 578 610—611
TCP theorem (TCP invariance), scattering amplitudes and      436 514—517
TCP theorem (TCP invariance), spectral condition and      151
TCP theorem (TCP invariance), spin-statistics theorem and      513 538 572—575
TCP transformation of      498—504
Tempered distributions (S*)      11—12 27 33 40 46—48 55—56 58 60—65 73 85 105—106 422-423(see
Tempered distributions (S*), analytic functions and      106
Tempered distributions (S*), field matrix elements as      249 422—423
Tempered distributions (S*), Fourier transforms      48 68—69
Tempered distributions (S*), radiation operators and      412—413 423
Tempered distributions (S*), terminological convention      48
Tempered growth      (see “Polynomial growth”)
Tempered sequences (Sf)      120
Tensor      122 247—250 344
Tensor field      250 252 264 270 499 501 527
Tensor product      196—197 206—207
Tensor, analytic function      481—486 492
Tensor, antisymmetric      342
Tensor, traceless symmetric      339—340
Tensor, under SL(2)      (see “SL(2) representations”)
Test functions, space of      (see “$\mathcal{S}$”)
Test functions, vector, tensor      248 261—262
Theta function $[\theta(x)]$      56—57 69 100—102 383 447—448 453 456 461
Theta function $[\theta(x)]$, projection operator      460—463
Theta function $[\theta(x)]$, smeared      392—394
Thirring, W., xviii      8 625 629 6 74
Three-particle space      152 204—205
Time reversal      110 164—165 177—178 180 191—192 241 320 322 323
Time reversal in homogeneous distribution formalism      343
Time reversal, charge conjugate spinor and      179
Time reversal, invariant distributions and      84—88
Time reversal, violation      498—499 (see also “Discrete transformations”)
Time-ordered product      3—4 359 382—383 396 464
Time-ordered product of currents      416—417
Time-ordered product, nomal product and      422
Time-ordered product, smeared $(T_{\chi})$      393—399
Time-ordered product, Wick $(T_{W})$      422
Timelike separation, notation      414
Titchmarsh, E. C.      523 632
Todorov, I. T., xvii      149 240 339 340 341 347 348 349 353 459 466 572 577 578 631—632 654 659 664 665 672 674
Toll, J. S.      510 545 576 634 655 659
Tolmachev, V. V.      577 628
Topological (continuous) group      212—214 242
Topology, topological space      18 22 24 25 28—29 212 586 598
Trace class      593 595
Trace of $\gamma$-matrix products      173
Trace of Pauli matrix products      134
Transformation law, of fields      (see “Covariance of
Transition probabilities      (see “Probability”)
Translation invariance      150 157 283 300 419 508 562 613 618
Translation invariance of state in $\textit{a}$      598—599
Translation invariance of TVEV      275
Translation invariance of Wightman functions      263 266—267
Translations      211 241 405 599
Transpose (transposition)      130
Tree, field-theory      620
Trivial (improper) subgroup      210
Trivial subspace      217
Trotter product formula      615
Trotter, H. F.      615 674
Truncated vacuum expectation value (TVEV)      272—281 374—378 386-388
Truncated vacuum expectation value (TVEV) of free fields      310
Tube $(T^{\pm})$      91 267 429 433 439—440 473—474 476 481—495 504—510 574
Tube, extended (      3 473—474 481—489 493 504—510 574
Tube, permuted, symmetrized      505—510
TVEV      (see “Truncated vacuum expectation value”)
Two-particle space      152 200—204
Two-point Function      269—270 284 286 337 363—364 532—533 553-554
Two-point function of free scalar field $D^{(\pm)}(x)$      99—100 309 334—336 363
Two-point function of free spinor field $[S^{(\pm)}(x)]$      318—319 335
Two-point function of generalized free field      330
Two-point function, covariant structure, and homogeneous distributions      345—349
Uhlmann, A.      241 352 658 674
Ultraviolet divergences      360—361 383 455 456 468 556 612 620
Umezawa, H.      242 352 466 543 632 655
Unbounded operator      (see “Linear operator” “Domain of “Algebra of
Unimodular group      (see SL(2))
Unit element      209 585 596
Unitarity, of S—matrix      2 407 411 417 428 515
Unitary operator      (see “Linear operator unitary”)
Units, choice of      7
Univalence      (see “Superselection rule univalence”)
Universal covering group      (see “Covering group”)
Universal enveloping algebra      147 223
Uretsky, J. L.      465 667
V — A current      500—501
VACUUM      111 151—152 193 248 256 296 351 362 406 407 599 608 609 619
Vacuum energy      619
Vacuum expectation value (vev)      260 274 281 318 351
Vacuum expectation value (VEV) of commutator      330—331
Vacuum expectation value (VEV) of current      441—442
Vacuum expectation value (VEV) of parafields      546—547
Vacuum expectation value (VEV) of radiation operator      412—413
Vacuum expectation value (VEV) of T-product      382—383 395—396 464
Vacuum expectation value (VEV), TCP transformation of      503—504
Vacuum in Haag’s theorem      550—551 555 560- 561 613
Vacuum polarization      561
Vacuum, anisotropy of      508
Vacuum, not annihilated by local field      530—531
Vacuum, space reflection and      324—325
Vacuum, uniqueness      151 257 272 276 283 292—294 297—301 351 618 619
Variation, bounded and total      20
Variational derivative      (see “Functional derivative”)
Vector field      250 423 561
Vector mesons      406
Vector potential      382
Vector space      13—14 584
Vector space, countably normed      21—29 105 115
Vector space, locally convex      598
Vector space, normed      13—21 105 “Nuclear
Vectors, notation      7 77
Vectors, representation of SL(2)      341—342 344
Vectors, state      (see “States”)
Velocity-space nonoverlap condition      384—389 396—399
Vertex part      562
VEV      (see “Vacuum expectation value”)
Vilenkin, N. Ya      31 32 42 105 106 269 339 340 353 577 628 629
Visconti, A.      242 352 632
Vladimirov, V. S.      75 96 106 332 353 429 445 467 508 509 574 575 632 637 675
Volkov, D. V.      576 675
Volume element, spherical coordinates      80
von Neumann algebra      4 582 584 587— 589 602—611 624
Von Neumann — Pontryagin — Montgomery theorem      214—215
von Neumann, J.      37 240 558 630 675
von Neumann’s theorem      558—559
w      (see “Pauli — Lubanski — Bargmann vector”)
W (invariant of Poincare group)      148 150 156
Watson, K. M.      8 629
Wave equation of field      337
Wave equation of field, first-order scalar      576
Wave equation of field, fundamental solution      77—82
Wave equation of field, higher spin      241—242
Wave function      336
Wave operators      422 556
Weak commutativity      257 299
Weak equivalence      595
Weak interactions      500—501 562
Weak local commutativity (WLC)      474 510—513 517—521 546—547 575
Weak topology, see Convergence, weak Weyl relations      559 569
Weidlich, W.      577 675
Weinberg, S.      242 352 468 642 675
Wentzel, G.      250 549 576 632
Westwater, M. J.      468 675
Wick ordering, see Normal product Wick polynomial      522—524 608—609
Wick, G. C.      205 240 242 327 652 658 675 676
Wick’s theorem      422
Wiener, N.      427 631
Wightman approach      3 243—301 350—353 362—363 399 575 582 607
Wightman functional      287—301
Wightman functions      246 260—286 287 291—292 351—352 464 487 562
Wightman functions and      265—268
Wightman functions in Haag’s theorem      552—554
Wightman functions of free fields      309—310 313 318—319
Wightman functions of infinite-component field      571
Wightman functions, analyticity      267—268 473 476 487 504—510
Wightman functions, charge conservation and      313
Wightman functions, gauge transformation and      311
Wightman functions, space-time inversion and      532—533
Wightman, A. S.      xvii 3 134 162 165 195 204 205 240 241 242 260 276 283 327 332 350 351 352 445 467 481 489 492 510 512 534 552 561 574 575 576 577 605 606 609 624 625 631 644 650 653 655 676 677 682
Wigner, E. P.      138 140 156 158 162 195 240 241 242 479 576 632 635 664 676 677 678
Wigner’s theorem      139 234—239 242
Williams, D. N.      486 574 663
Wilner, M.      468 639 668
Winogradzki, J.      241 678
Wizimirski, Z.      283 351 678
WLC      (see “Local commutativity”)
WLC and      510—512
Wray, J. G.      468 668 678
Wu, C. S.      575 658
Yaglom, A. M.      242 252 577 645
Yang — Feldman equations      358 382 383 390—392 415 417—419 464
Yang, C. N.      464 517 575 658 679
Yndurain, F. J.      539 576 644
Young patterns      526
Yukawa potential      281
Yukawa theory      453—463 620—623 626
Zaikov, R. P.      353 674
Zav’yalov, O. I.      577 673 679
Zhelobenko, D. P.      242 632
Zimmermann, W.      381 401 464 465 467 468 607 625 638 645 658 659 679
Zumino, B.      576 660
“Almost everywhere”      47
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