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Deligne P., Kazhdan D., Etingof P. — Quantum fields and strings: A course for mathematicians (Vol. 1)
Deligne P., Kazhdan D., Etingof P. — Quantum fields and strings: A course for mathematicians (Vol. 1)

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Название: Quantum fields and strings: A course for mathematicians (Vol. 1)

Авторы: Deligne P., Kazhdan D., Etingof P.

Аннотация:

Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics.
In 1996 — 97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose is eloquently stated in a letter written by Robert MacPherson: "The goal is to create and convey an understanding, in terms congenial to mathematicians, of some fundamental notions of physics ... [and to] develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra."
These volumes are a written record of the program. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the program. The book also includes problems and solutions worked out by the editors and other leading participants. Interspersed are mathematical texts with background material and commentary on some topics covered in the lectures.
These two volumes present the first truly comprehensive introduction to this field aimed at a mathematics audience. They offer a unique opportunity for mathematicians and mathematical physicists to learn about the beautiful and difficult subjects of quantum field theory and string theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 723

Добавлена в каталог: 19.06.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\beta$-function      10 568 574 583 779 1163 1292 1306 1368 1379 1390 1433 1451ff
$\gamma$-runction      779 783
$\sigma$-model      7 211ff 263ff 279ff 437 492ff 773ff 895 1171ff 1183ff 1292ff 1313ff
$\sigma$-model, twisted      802 1324
$\theta$-dependence      1213
$\theta$-term      7 306 210 223 326 335 1252 see
$\zeta$-runction regularization      185ff 483 673 678 737 855ff
${\phi}^{3}$-theory      423 435 621 782
${\phi}^{4}$-theory      440 444 456 571 576 626 629
't Hooft loop      36 1255ff
1-loop      570 577 625 783ff 868 971ff 975ff 1308ff
1-particle irreducible      429
1-particle irreducible, correlation Function      704
1-particle irreducible, effective action      773
1-particle irreducible, graphs      1187
action      7 143 729 817 see
Action, effective      see “Effective action”
Amdiiary variable      237 1095
Anftatz      8
Anomaly      8 740 885 901 1166ff 1297 1432 1447ff 1463 1464 1489
Anticfairal      252
Antiinstanton      1213 1236
asymptotic freedom      8 469ff 570 788 1440
Asymptotically free theory      576 1151 1348
Background (field)      9 780 9038
Bare, coupling      592 780
Bare, mass      430 644
Beltrami, differential      852ff
Beresin integral      483 744
Beretmian      59ff 83 612 619
beta function      see “$\beta$-function”
Bethe anaats      800
Born aitproadmation      464
Bose field      10 236
Bose — Fexmi comspoD fence      1199ff 1205ff
Boson      10
Boson, Goldstone      187 1139 1142ff 1342 1344 1411
BPS (state)      9 1283ff 1370ff
BPS (state), classical      9 1281ff
BPS (state), formalism      1358f
BPS (state), monopole      1289
BRST      9 878ff 1061ff
BRST, charge      961
BRST, cohomology      880 1162ff
BRST, current      961
BRST, differential      879 1161 1162
BRST, quantization      871ff 961ff 1159ff
Calabi — Yau manifod      740 789 912 11058 1292 1305 1333
Cartan model      1264ff
Central'charge      see “Charge central”
Chan — Paton rules      841ff 937
Charge, central      11 858 10436" 1295 1359
Charge, density      202 541
Charge, Noether      see “Noether charge”
Chera — Simon term      216 612 660 1233
Chiral      11
Chiral, algebra      1025ff 1045 1049ff 1067ff 1082ff
Chiral, operator      1488 1492
Chiral, ring      1334ff 1453
Chiral, superadd      252 259 635 1417
Chiral, symmetry      1200
Classical, field      11 155ff
Classical, limit      12
Classical, solutions      161
Classical, vacuum      183ff
Clifford modules      107ff 232
Coleman — Mandiila theorem      1176 1176
COLOR      1432
Compactification      12 738ff 1098 1106
Component field      34 236S
Composite operator      448 452 455 576
confinement      12 1195 1220ff 1258ff 1271 1345 1433 1448
Conformal blocks      1031ff 1084ff
Conformally invariant (confornal) field theory      459 727ff 824ff 874ff 1017ff 1203
Conserved current      12 176 825 1154
Convergence, superficial      432
Correlation function      12 447 453 741 1031ff 1131 1318
Correlation function, (n-point)      421 731
Coulomb, phase      13 1260
Coulomb, potential      1194 1236
Counterterm      13 430 441 442 569
Coupling      13 436 784
CPT      392ff
Critical, coupling      1163
Critical, dimension      437
Critical, field tbeoiy      440 452
Current      13 162 1201
Cutoff      13 560 1173
Cutoff function (cutoff propagator)      441 455 557
D-modules      1020ff
Debye screening      1237
Deligne cohomology      218ff
Dilatino      933 1101 1105
Dilaton      1052
DIMENSION      153
Dimension, of a field      451
Dimension, of an operator      14
Dimension, of an operator, anomalous      14 580ff 629 1415
Dimension, of an operator, engineering      14 446 567
Dimension, of an operator, quantum      14 451
Dimension, scaling      14 446
Dimensional, reduction      14 187ff 245ff 276ff 291ff 331
Dimensional, regularizaiion      560 564 566 597ff 673 781ff 897
Dimensional, transmutation      592 1433
Dirac fermions (Dirac tpinors)      32 744
Dirac operator      196 235 477ff 489ff 497ff 614 628 891 1100
Divergence (logarithmic, linear, quadratic, superficial)      429 431 436 443 786 1173
Donaldson theory      645 1392ff
Duality      14 1225ff 1456 1488
Dynkin diagram      101
Dytiamical, mass generation      585ff
Dytiamical, symmetry breaking      585ff
Dytiamical, variable      15
Effective, action      15 777ff 908ff 1097 1101 1101ff 1187 S241415
Effective, coupling      564 566
Effective, cross-sectional area      463
Effective, lagrangian      15 556 1112 1161 1207 1423
Effective, potential      15 1123 1429 1442 1444 1446
Effective, theory      15 586 1186ff 1394ff
Electric charge      15 209
Electromagnetic duality      1240 1354ff 1454ff
electromagnetic field      145 201ff 540 1193
Electron      16
Elementary field      see “Field elementary”
Elliptic curve      744 1368 1376 1376ff 1483
Elliptic genus      1330
Energy-momentum tensor      16 176ff 750ff
Euclidean action      221ff see
Euler — Lagrange equations      16 537 653 657 692 1249
expectation value      16 495
Faddeev — Popov, determinant      855 873 1228
Faddeev — Popov, ghosts      871ff
Faddeev — Popov, method      16 796
Fayet — Hiopoulo B term      308
Fermi field      10 236
Fermion      10 744 943 947 1199 1202 1447
Fermion, Goldstone      633
Feynman — Kac formula      672 732 791 1128
Feynman, diagrams (graphs)      17 426 465 561 589 605 674 682 685ff 701 814 865ff 978ff 1187ff
Feynman, diagrams (graphs), amphtude      865ff
Feynman, famous formula      427
Feynman, integral      424ff 597ff 729
Field      17
Field, auxiliary      see “Auxiliary variable”
Field, background      see “Background field”
Field, classical      see “Classical field”
Field, component      see “Component field”
Field, elementary      11 16
Field, local      see “Local field”
Field, strength      17
Flavor      1341 1434 1439ff
Fock space      18 503 527 745 631ff 876ff 919
Free, classical electrodynamics      198ff 201ff 396
Free, Classical field theory      191ff 395 539
Free, QFT of arbitrary spin      398
Free, quantum field tltcon      18 449 523ff 1205
Free, scalar QFT      192 397 526ff
Free, spinor QFT      195 398
Functional determinant      855 884 891
Galilean group      151
Gauge      18 837
Gauge, boson      18
Gauge, field      18
Gauge, fixing      1096
Gauge, group      18
Gauge, theory      201ff 438 1191
Gauge, theory, abelian      198ff 201ff 1209ff
Gauge, theory, nonabelian      1432ff
Gauge, transformation      10 793
Gauging a symmetry      19 175ff 1152
Gaugino      1101 1105
Gaussian, integral      19 731 1423
Gaussian, measure      402
Ghort      19 833ff 1163
Ghost number      1164
Gluon      20 1445
Goldstone boson      see “Boson Goldstone”
Goldstone fermion      see “Fermion Goldstone”
Goldstone theorem      1136
Grassmaniann variables      41ff
Grassmannian      1071ff 1183ff
Gravitational field      20 156 180ff 542
Gravitino      920 933 1101 1105
Graviton      840
Gravity      542ff
Green's function      891
Gross — Neveu model      587ff
GSO projection      927ff 945
Haag — Ruelle scattering thaory      407ff
Hamiltonian      20 172 480 537ff
Hamiltonian, formalism      20 163ff 486 537ff
harmonic oscillator      487 520 523ff 620 622 733
Heisenberg algebra      1049ff
Helicity      20
Heterotic string      941ff 110ff
Higgs mechanism      20 185ff 645 1232 1259
Higgs phase (regime)      1218ff 1260
Higher derivative term      20
Hypermuttiplet      1374 1387 1396
Imaginary time      221 891
Index of elliptic operator      475ff 691 695
Instanton      21 1210 1212 1235 1440
Instanton, gas      1211 1236
Integral, density      154 239
Integral, form      84ff 154
Integrating out      21 922 1232
Interaction      21 452 456
IR (infrared)      1331
IR (infrared), behavior      1141 1171ff 1209 1343 1489
IR (infrared), limit      21 1155
IR (infrared), stable fixed point      1344
Jost'a theorem      387
Kac — Moody algebra      739 1049ff
Kalosa — Kletn      I095ff
Kinetic term      21
Klein — Gordon, equation      526
Klein — Gordon, popagator      422
Lagrangian      21 162ff 198 611ff 1206 1226 1341 1345 1348 1353 1362 1363
Lagrangian, denity      21 143 157ff 237ff 696 1127 1132
Lagrangian, effective      see “Effective lagrangian”
Lagrangian, formalism      21 537ff
Landau singularity      374
Landau — Ginzburg      1300 1327ff
Large N limit      22 388ff 1171ff 1183ff 1404 1405
Lehhmann — Symanzik — Zimmermann (LSZ) formalism      864
Lightcone      12
Lightcone, gauge      22 837 986
LIMIT      see “Classical limit
Lippmann — Schwinger equation      463
Little group      22
Local, field      156
Local, functional      445ff
Local, operator      1336
Local, symplectic form      368
localization      1267
Loop, group      792
Loop, space      497ff
Lorentz, invariance      547
Lorentz, metric      358
Low energy      23
Low energy, behavior      23 1352ff
Low energy, effective Lagrangian      23
Low energy, effective theory      23
Low energy, limit      23
Magnetic, charge      23 209
Magnetic, theory      1454
Majorana spinor      32 929
Majorana — Weyl spinor      929 1101 1105 1108
Manifest symmetry      169
Marginal, interaction      1171
Marginal, perturbations      1294
Mass      23
Mass, gap      1202 1342 1345 1348 1433 1437
Mass, spectrum      383
Massless, scalar      735
Massless, spinor      744
Maxwell theory      23 201ff 540ff 1225
Minimal, coupling      19
Minimal, subtraction      782ff 787ff
Minkowski space      23 150 191 358
Modular form      1242
Moduli space of vacua      24 38
Moduli space of vacua, classical      24 185 304ff 1349 1302 1428 1434ff 1463 1467 1469
Moduli space of vacua, quantum      24 1366ff 1429 1436ff 1445 1469 1470 1476
Moment map      147 1268 1421
Momentum      24 148
Momentum, transfer      464
monopole      24
Neveu — Schwarz sector      24 745 918ff
Noether, charge      25 147ff 170 359
Noether, current      25 147ff 170 175 193 362
Noether, theorem      147 165ff 825
Nonlinear $\sigma$-model      211ff 267ff 895ff
Nonperturbative effect, result      25
Nonrenormalizable field theory      558 1141
Normal ordering      402 448 452
Observable      25 515
Octonions      133ff
Off-shell      25 161
On-shell      25 161
One-loop      see “1-Ioop”
Operator      26 see operator”
Operator product expansion (OPE)      25 449ff 456ff 794 825 964 1453
Operator, composite      see “Composite operator”
Orbifolding      1301
Particle, quantum      26
Particle, relativistic      26
Partition function      27 1186 1227 1241 1270ff
path integral      27 481ff 505ff 623 624 681 691ff 1172 1218ff 1227 1231 1256
Pauli — Villars regulator fields      1168
Perturbation expansion      27 185 421ff 424ff
Perturbation theory      27 524ff 955ff 1440
Phase shift      462
Phase transition      559
Photon      28 540
Planck length      1096
Poincare, algebra      28 359
Poincare, group      151 379ff 1112
Poincare, group, positive representation of      422
Poisson brackets      148 170 359 367 372
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