Ticciati R. — Quantum field theory for mathematicians :: Электронная библиотека попечительского совета мехмата МГУ

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Ticciati R. — Quantum field theory for mathematicians

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Название: Quantum field theory for mathematicians

Автор: Ticciati R.

Аннотация:

Ticciati's approach to quantum field theory falls between building a mathematical model of the subject and presenting the mathematics that physicists actually use. It begins with the need to combine special relativity and quantum mechanics and culminates in a basic understanding of the standard model of electroweak and strong interactions. The book is divided into five parts: canonical quantization of scalar fields, Weyl, Dirac and vector fields, functional integral quantization, the standard model of the electroweak and strong interactions, renormalization. This should be a useful reference for those interested in quantum theory and related areas of function theory, functional analysis, differential geometry or topological invariant theory.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 714

Добавлена в каталог: 01.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Lorentz tensors      163
Lorentz-invariant functions      111—113
Lowering operator of Lie algebra      145
Lowering operator, harmonic oscillator      15
Lowering operator, su(3)      448
LSZ reduction formula      282—285 504
LSZ reduction formula, Dirac fields      302—306
LSZ reduction formula, matrix elements      517
LSZ reduction formula, unstable particles      318
LSZ reduction formula, vector fields      309—310
Magnetic moment operator      490
Majorana, field      209
Majorana, mass term      171
Majorana, representation      209 232 239 523
Majorana, spinor      204
Mandlestam parameters      114
Mandlestam plot      115
Marginal operator      668
Mass      4
Mass dimension      119 218 545
Mass dimension, coupling constants      545
Mass dimension, ERG      667
Mass dimension, Feynman integral      597
Mass dimension, Green function      634
Mass matrix, fermionic      200
Mass matrix, gauge fields      403
Mass matrix, scalar fields      402
Mass, amplitude pole      115
Mass, amplitude suppression      518
Mass, eigenquark      470 518
Mass, hierarchy problem      663
Mass, hyperboloid      6
Mass, renormalization condition      292—294
Massive vector field      248
Matrix element      17
Matrix element, Lorentz group action on      17 137
Matrix element, SU(2) invariance      499
Matrix groups      54
Matrix representation of Lie algebra      146
Matrix representation, Lorentz group      137 164
Matter current      391
Matter current, covariant conservation      392 425
Measure on moduli space      381
Medium strong interactions      492
Meson      443 480
Meson, axial isosinglet mixing      494
Meson, matrix      486
Meson, structure      483—484
Metric      2
Minimal coupling      266 387
Minimal subtraction      540 593
Mode counting      514
Moduli space      376
Moduli space, parametrization      403
Momentum operators      2
MS renormalization      540 640
MS renormalization, global symmetries      605
MS renormalization, QED      593
Multiplet, gauge fields      385
Multiplet, matter fields      389
Noether      see "Conserved current and quantity"
Non-perturbative view      272
Non-renormalizable theories      605
Non-renormalization of Lagrangian parameters      616
Normal ordering      28 49 181 217
Normal ordering, Fermi fields      186
Normalization of fields      290
Nucleon parton content      514
Nucleon-pion Lagrangian      498
Nucleon-pion scattering      499
Number operator      16
O(1, 3)      see "Lorentz group"
Off-shell modes      247
One-particle irreducible      see "1PI"
One-particle states      277
One-particle states, chiral Dirac operator      366
Operator determinants      341 365
Operator determinants, Jacobian      380
Operator insertion      554
Operator ordering      43 335—336 346
Operator product expansion      553
Optical theorem      132
Orbital angular momentum      183
Orthogonal group      54
Parallel transport      264
Parallel vector fields      264
Parasiuk      600
Parity      72—73
Parity and angular momentum      235
Parity, Dirac fields      233—236
Parity, pions      498
Parity, so(1, 3) representations      162
Parity, Weyl spinors      169
Parton model      509—514
Pauli matrices      148
Pauli — Villars regularization      542
Peccei — Quinn mechanism      477
Permutation group $S_{3}$       484
Perturbation theory      80—94 103—108
Perturbation theory, resummation      290
Photon mass non-renormalization      616
Photon mass regularization      568
Photon self energy      613
Physical, Lagrangian      288 566
Physical, parameters      288
Physical, state      3
Physical, vacuum      274
Pions      497
Pions, Goldstone bosons      501
Pions, parity      498
Planck constant      1
Plane-wave limit      284
Poincare group      8
Poincare group, unitary representation      9
Poisson bracket      23 27
Poisson bracket and symmetry      47
Polarization average      254
Polarization spinor      see "Dirac polarization spinor" "Weyl
Polarization sum      254
Polarization vector      251
Polarization vector, completeness relations      251
Polarization vector, normalization relations      251
Polchinski      669
Pontrjagin index      431 473
Position operators      2
Position operators, axioms      9
Primitive divergence      564 601
Proca equation      248
Propagator      106
Propagator, Schwinger representation      534
Proper subdiagram      600
Pseudoscalar field      72
Pseudoscalar mesons      481
Pseudoscalar mesons, table      444
PT symmetry      77
PT symmetry, strong interactions      523
Pure spin kets      153
QCD      454 465—468
QCD, abelian anomaly      503
QCD, axial U(1) anomaly      475—478
QCD, chiral symmetry      475
QCD, running of $\alpha_{s}$       658
QED, charge renormalization      568—573
QED, effective classical action      610—612
QED, electron renormalization      579—581
QED, electron self energy      578—579
QED, ERG      669
QED, finite resolution of apparatus      589
QED, gauge invariance      615—617
QED, infrared divergence      587—590

QED, lagrangian      565—566
QED, massive photon      253—256 372
QED, massive photon and scalar      360
QED, Pauli — Villars regularization      542
QED, photon renormalization      576—577
QED, photon self energy      573—576
QED, problem with cutoff-regularization      313
QED, propagator      382
QED, quantization      381—384
QED, renormalized vertex function      590
QED, RGE      652
QED, Routhian      383
QED, running of a      654
QED, vertex correction      582—587
Quantum field      12 17—22
Quantum field, Lorentz group action on      137
Quantum gravity      664
Quantum numbers      50 67—69
Quarks      438 465 480
Quarks, decays      520
Quarks, mass terms      468
R gauge      405
Raising operator of Lie algebra      145
Raising operator, harmonic oscillator      15
Raising operator, isospin      521
Rank of Lie algebra      145
Real action      38
Real action, classical fields      45
Real action, classical mechanics      40—41
Real action, infinitesimal      39 42 43
Real field      52
Real representation      163
Regularization      118
Regularization, axial current      476
Regularization, composite operators      552—554
Regularization, cut-off      541
Regularization, dimensional      543 551
Regularization, fermionic functional derivative      419
Regularization, parameter      296
Regularization, Pauli — Villars      542
Regularization, QED photon mass      568
Regularization, the principle      538
Regularization, trace      420 423
Relativity      13
Relevant operator      668
Renormalizable interactions      119
Renormalizable theories      605
Renormalization      116
Renormalization conditions      117 287 291
Renormalization conditions, coupling example      299—301
Renormalization conditions, Dirac fields      306—309
Renormalization conditions, gauge invariance      567
Renormalization conditions, mass and field example      295—296
Renormalization conditions, QED      567—568
Renormalization conditions, unstable particles      317
Renormalization conditions, vector fields      311—313
Renormalization group      632
Renormalization group equation      see "RGE" "ERG"
Renormalization part      601
Renormalization part, disjoint      603
Renormalization part, nested      603
Renormalization part, overlapping      604
Renormalization, $z_{e} = z_{\psi}$       568—573
Renormalization, composite operators      554—557
Renormalization, Dirac fields      302—309
Renormalization, example      295—301
Renormalization, gauge invariance      623—629
Renormalization, operator mixing      556
Renormalization, scalar fields      291—295
Renormalization, the principle      540
Renormalized propagator      293 311
Renormalized propagator, analyticity      316
Renormalized propagator, spectral function formula      316
Renormalized, coupling      118
Renormalized, field      118 278
Renormalized, Green function      281 287—290
Renormalized, mass      118
Representation      see "Hermitian" "Group" "Lie "Matrix" "Unitary
Repulsion between like charges      258
Resonance      102
Restriction of representation      145
RGE      632 634
RGE and ERG      668
RGE, $\phi^{4}$ -theory      644—652
RGE, fixed points      659
RGE, Green functions      660
RGE, high energy behavior      661
RGE, leading logarithm      652
RGE, matter fields      656
RGE, perturbative      640—643
RGE, QED      652
RGE, Yang — Mills theory      655
Rigged Hilbert space      3
Ronthian      373
Root diagram      146
Roots      146
Roots, su(3)      441
Rotation of Weyl spinors      167
Rotation symmetry      37—40
Running coupling parameter      649
Running coupling parameter, $\alpha$ in QED      654
Running coupling parameter, $\alpha_{s}$ in QCD      658
Rutherford scattering      130
S matrix      80 83—84 95 281
s, t, u channels      115
Scalar field      17—22 72
Scalar field, axioms      18
Scalar field, free      19
Scalar field, Lorentz transformation      18
Scalar nucleon-meson theory      95—102
Scalar potential      401
Scalar QED with massive photon      255
Scalar self energy      312
Scalar self energy, QED      567
Scale invariance      633
Scale invariance, bare Lagrangian      635—639
Scattering, $eN \rightarrow eX$       512
Scattering, $e^{+}e^{-}$ annihilation      515
Scattering, $p\pi^{+} \rightarrow p\pi^{+}$       501
Scattering, $p\pi^{-} \rightarrow p\pi^{-}$       501
Scattering, amplitude      80 108
Scattering, fermion-scalar      227—230
Scattering, high-energy approximation      228
Scattering, photon-photon      592 615
Schroedinger picture      81
Schur's lemma      451
Schwinger representation of the propagator      534
Schwinger term      553
Self energy      294
Self energy, Dirac field      307
Self energy, renormalized      295—298
Self energy, spectral function formula      317
Self energy, vector field      311
Semi-simple Lie group      387
Shape state      30
Simple Lie group      387
Simple Lie group, topology      430
sl(2, $\mathbb{C}$ )      148
Slavnov — Taylor identity      622
SO(1, 3)      54
so(1, 3) and SL(2, $\mathbb{C}$ )      168
so(1, 3), $\gamma$ matrix representation      210
so(1, 3), complexification      149
so(1, 3), exponentiation      56
so(1, 3), representations      159—164
SO(2) symmetry      48—53
SO(3)      148
SO(N)      54
Source - time-dependent      95
Source - time-independent      97

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