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| Ticciati R. — Quantum field theory for mathematicians |
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| Предметный указатель |
effective Lagrangian 654
Effective propagator 289
Eigenstate 3
Eigenstate, expansion 3
Elastic scattering 90
Electron mass 459
Electroweak see "Weinberg — Salam model"
Energy counterterm 98 117
Energy-momentum 65
Energy-momentum,  function 107
Energy-momentum, operator 4 16 64
Enveloping algebra 492
Equal-time anti-commutation relations 179 215
Equal-time commutation relations 21
Equal-time commutation relations, averaged 32
Equal-time commutation relations, complex field 51
Equal-time commutation relations, scalar field 27
Equal-time commutation relations, vector field 251
Equations of motion see also "Euler — Lagrange equation" "Hamilton "Heisenberg
Equations of motion for quantum fields 413—414
Equivalent representations 142
Erg 665
ERG and RGE 668
ERG, fixed point 666
Euler — Lagrange equations, classical fields 25
Euler — Lagrange equations, classical mechanics 22
Euler — Lagrange equations, Fermi fields 173
Euler — Lagrange equations, Weyl spinors 174
Euler — Lagrange equations, Yang — Mills theory with fermions 392
Evanescent operator 559
Exact renormalization group see "ERG"
Exchange potential 111
External symmetries 47
Faddeev — Popov determinant 377 381 393
Faddeev — Popov Lagrangian 381 382 395
Faddeev — Popov principle 372 379 410
Faddeev — Popov principle, 2d example 376—378
Faddeev — Popov quantization 393—398
Faddeev — Popov quantization, delicate points 407—410
Faddeev — Popov quantization, QED 381—384
Family-number conservation 464
Fermi loop rule 194—195 219 370
Fermi statistics 179
Fermion 164
Fermion, currents 461
Fermion, mass matrix 200
Fermion, masses 200—204
Fermion, number 217
Fermionic calculus 171—173
Fermionic functional derivative 364
Fermionic functional derivative, regularized 419
Feynman diagram 103
Feynman diagram, derivative of 570 602
Feynman integral 105
Feynman integral, Euclidean form 535—538
Feynman integral, mass dimension 597
Feynman integration trick 297 300 533
Feynman parameters 534
Feynman parameters, scaling trick 584
Feynman rules 103—108
Feynman rules, derivation 103—108 351—355
Feynman rules, derivative interaction 355
Feynman rules, Dirac fields 219
Feynman rules, gauge theory 396
Feynman rules, kinetic counterterm 289
Feynman rules, massive photons 253
Feynman rules, unstable particles 318
Feynman rules, Weyl spinors 191—197
Field renormalization 277
Field renormalization factor 277
Field renormalization factor, spectral formula 315
Field renormalization, condition 292—294
Fierz transformations 224—227
Final state, three particles 126
Final state, two particles 124
Finite-volume approximation 121
First-order Lagrangian 374 375 384 394
Flavor SU(3) 443—444 524
Flavor SU(3), applications 488—497
Flavor SU(3), chiral 530
Flavor SU(3), formalism 485—488
Flavor symmetry 438 471
Fock space 14 179
Forest 604
Forest formula 602—605
form factors 523
Formal  theory 294 608
Forward wave 132
Four-component spinor see "Dirac polarization spinor" "Dirac
Four-Fermi interactions 461 507
Fourier transform 2
Fourier transform of inner product 343
Fourier transform of operators 343
Fourier transform, functional calculus 334
Free field, Dirac spinor 215
Free field, scalar 19
Free field, vector 250—252
Free field, Weyl spinor 177
Free vacuum see "Vacuum"
Front-back asymmetry 465
Fujikawa's anomalous Jacobian 423
Functional derivative 25 26
Functional derivative, fermionic 364 419
Functional Fourier transform 334
Functional integral quantization 328 346
Functional integral quantization, complex fields 349
Functional integral quantization, covariance 344
Functional integral quantization, derivation 329—331
Functional integral quantization, Fermi fields 367—369
Functional integral quantization, Feynman rules for fermions 369—370
Functional integral quantization, free particle 332—335
Functional integral quantization, Green functions 349
Functional integral quantization, Hamiltonian form 342 356—358
Functional integral quantization, Lagrangian form 342 347—349
Functional integral quantization, massive vector field 359—361
Functional integral quantization, matrix of propagators 345 358
Functional integral quantization, perturbation theory 351—355
Functional integral quantization, principle for Fermi fields 367
Functional integral quantization, Routhian form 373
Functional integral quantization, stationary phase 336
Functional Jacobian 379
Functional measure 33 380
Functional proof of Ward identity 561
Gauge 262
Gauge field 264 265 389
Gauge field, electroweak 456
Gauge field, topology 433—435
Gauge fixing 376
Gauge fixing, condition 379
Gauge fixing, term 382
Gauge group 385
Gauge group, topology 432—433
Gauge invariance 262
Gauge invariance of Lagrangian 266
Gauge parameter non-renormalization 616
Gauge theory 248
Gauge theory, geometry 262—265 384—390
Gauge theory, Routhian 394
Gauge transformation 385 387 392
Gauge transformation, infinitesimal 392
Gauge, principle 262 265 385
Gauge, symmetry 248
Gauged SU(2) 409
Gaussian functional integrals 340
Gaussian Integrals 339
Gell-Mann basis for su(3) 440
Gell-Mann — Okubo formula 493
Generalized momentum see "Canonical momentum"
Generating functional 270 271
Generation mixing 471
| Generation of lepto-quarks 470
Generator 39 48
Generator, exponentiating 56
Ghost field 395
Ghost number 626
Global analysis 428 430—431
Global anomaly 428 436
Global anomaly, Standard Model 475
Global symmetry 384
Gluons 444 465
Goldberger — Treiman relation 503 531
Goldstone boson 53 398 399
Goldstone theorem 401—402
Gordon relations 523 585
Graded algebra 362
Grand unified symmetry 69
Grand unified theories 478 671
Grassmann algebra 361
Green function 271
Green function as VEV 274
Green function, computing 272
Green function, connected 292
Green function, n-point 271
Green function, renormalized 281
Gribov ambiguity 409
Ground state 15
Group - dimension of 56
Group action 41
Group representation 58
Group representation, tensor product 154
Haag's theorem 84
Hadron 444
Hadron, EM mass splitting 495
Hadron, multiplets 481—483
Half-life 129
Hamilton equations 23 26 27
Hamiltonian 4
Hamiltonian classical fields 26
Hamiltonian classical mechanics 23
Hamiltonian Dirac field 215
Hamiltonian form of the action 23 26
Hamiltonian free scalar field 28
Hamiltonian quantum oscillator 15
Hamiltonian vector field 250
Hamiltonian Weyl field 178
harmonic oscillator 14—16
Heisenberg equations 23 24 28 421
Heisenberg picture 82
Helicity 174 181—182
Helicity, basis 216
Helicity, table 182
Hepp 600
Hermitian covariant derivative 264
Hermitian generators 388
Hermitian representation 61 147
Higgs fields 455
Higgs mechanism 398 401 403—404
Holomorphic extension of a representation 149
Homomorphism of Lie algebras 141
Hopf degree theorem 430
Hypercharge 443 456 467 481
Ideal state 3 80
Identity representation 439
Imaginary time 339
Impact parameters 512
In and out states 277—281
Infrared divergence 564 587—590 601
Infrared momentum cut-off 588
inner product of functions 343
instantons 474
Interaction picture 82—85
Internal angular momentum 183
Internal symmetries 47
Intrinsic parity 72 235
Invariant, amplitude 107
Invariant, density of final states 122
Invariant, inner product 387
Invariant, subspace 143
Irreducible representation 144
Irreducible representation of SU(3) 445 450
Irrelevant operator 667
Isomorphic representations 142
Isomorphism of Lie algebras 141
Isospin 443 481 497 521
Isospin, multiplets 482
Isospin, raising operator 521
Isotropic tensors 111 447
Jacobi identity 140
Kaon decays 519
Kets 3 4
Kets, Lorentz normalization 7
Kets, phase ambiguity 175 214
Kets, pure spin 153
Klein — Gordon equation 21 26 174 205 248
Klein — Gordon operator 207
Klein — Nishina formula 261
KM matrix 470 518 520 522 525
KM matrix, bounds on  522
KM matrix, bounds on  522
Lab frame 125 259 510
Lagrangian bare 288
Lagrangian classical fields 25
Lagrangian classical mechanics 22
Lagrangian non-polynomial 665—671
Lagrangian QCD 467
Lagrangian renormalized 288
Lagrangian scalar-neutrino theory 188
Lagrangian vector field 247—249
Lagrangian Weyl spinors 173
Lamb shift 592
Landau gauge 567
Least-action principle 22
Left-right asymmetry 464
Legendre transform 76
Legendre transform, Fermi fields 173
Lepton families 464
Lepton number 473
Lepton number, violation 473
Lie algebra 55 141
Lie algebra representation 61 140 141—147
Lie algebra representation, holomorphic extension 149
Lie algebra representation, so(1, 3) 159
Lie algebra representation, su(2) 150—153
Lie algebra representation, tensor product 154—158
Lie algebra, actions 57
Lie algebra, complexification 388
Lie algebra, direct sum 141
Lie bracket 60 139
Lie subalgebra 141
Local averaging 31
Localized state 278
Logarithmic divergence 117
Longitudinal photon 247 248
Loop diagram 116 254 296
Loop integral 117 300 533—535
Loop integral, imaginary part 134
Loop momenta 116
Lorentz action 137
Lorentz action on Dirac fields 215
Lorentz action on Dirac spinors 214
Lorentz action on matrix elements 17
Lorentz action on scalar fields 18
Lorentz action on Weyl fields 167
Lorentz action on Weyl spinors 177
Lorentz action, infinitesimal 65
Lorentz group 54
Lorentz group, connected 54
Lorentz group, matrix representation 137
Lorentz group, unitary representation 7
Lorentz invariant measure 6
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