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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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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 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 “ Test functions, vector, tensor 248 261—262 Theta function 56—57 69 100—102 383 447—448 453 456 461 Theta function 460—463 Theta function 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 393—399 Time-ordered product, Wick 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 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 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 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 99—100 309 334—336 363 Two-point function of free spinor field 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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