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

$g_{A}$       525 527 529
$G_{F}$       463
$g_{V}$       525 527 529
$\beta$ decays      525—530
$\beta$ function      642
$\beta$ function at two loops      658
$\Delta^{++}$       501
$\Gamma$ function      548
$\gamma$ matrices      205 207
$\overline{MS}$ renormalization      594
$\phi^{3}$ -theory      295
$\phi^{3}$ -theory, renormalization      295—301
$\phi^{4}$ -theory      93 668
$\phi^{4}$ -theory, normal ordering      29
$\phi^{4}$ -theory, renormalization      270—294
$\phi^{4}$ -theory, RGE      644—652
$\sigma$ model      502
$\sigma$ Model, abelian anomaly      503
$\theta$ vacua      435
'Later on the left' rule      191 219
't Hooft gauge      406
1PI diagram      292
1PI Green function      292 294 295
1PI Green function, RGE      661
Abelian anomaly      419—425 553
Abelian anomaly theorem      421
Abelian anomaly, $\sigma$ Model      503
Abelian anomaly, QCD      476 503
Abelian anomaly, Ward identity      561
Abelian Lie algebra      144
Action of Lie algebra      57 141
Action, Lorentz group      137
Adjoint action      138
Adjoint representation      142
Affine connection      263
Alternating tensors      361
Amplitude      107
Amplitude, interference      197
Amplitude, relative sign      194 219
Amplitude, trace trick for squaring      197
Angular momentum and parity      235
Angular-momentum operator      66 182 183—185
Annihilation operator      16
Annihilation operator, time-dependent      21
Annihilation operator, wave-packet      279—280 303 310
Anomalous Jacobian      423 476 629
Anomalous magnetic moment      591
Anomalous symmetry      412
Anomaly      49
Anomaly, axial rotation      424
Anomaly, axial U(1)      475—478
Anomaly, BRS current      629
Anomaly, chiral coupling      426
Anomaly, fermion currents      415—417
Anomaly, lepton and baryon numbers      473
Anomaly, local      425—428
Anomaly, massless fermion      436
Anomaly, scalar theories      414
Anomaly, Standard Model      471
Anomaly, trace condition      427
Anomaly, triangle diagram      428
Anomaly, vector coupling      425
Anti-particle      71
Anti-symmetric Lorentz tensors      163
Anti-symmetric representations of SU(3)      450
Anti-unitary operator      74
Arcwise connected      429
asymptotic freedom      656 657
Asymptotic series      258
Atiyah — Patodi invariant      365
Attraction between opposite charges      258
Axial current      558—562
Axial current, regularization      476
Axial current, Schwinger regularization      552
Axial gauge      383 393
Axial U(1) anomaly      475—478
Axial-vector mesons      481
Axial-vector mesons, leptonic decays      496
Axion      478
Background Dirac field      301
Background field      270
Bare Lagrangian      288
Bare Lagrangian, non-dependence on renormalization scheme      639
Bare, coupling      118
Bare, field      117
Bare, mass      118
Bare, parameters      288
Baryon      480
Baryon $\beta$ decays      525—530
Baryon decuplet      481
Baryon number      470
Baryon number, violation      473
Baryon octet      481
Baryon octet, magnetic moments      488—491
Baryon octet, matrix      486
Baryon, quark wave functions      490
Baryon, structure      484—485
Berezin      619
Bianchi identities      431
Binomial ordering      335
Block-diagonal form      389
Bogoliubov      600
Bohm — Aharanov effect      249
Boost of Weyl spinors      167
Born approximation      110 111
Bose symmetry      14
Bosons      164
Box operator      21
BPHZ procedure      600
Breit — Wigner peak      325
Bremsstrallung      589
BRS current anomaly      629
BRS transformation      617—619
BRS transformation, matter fields      628
BRS variation      619
BRS variation, Faddeev — Popov action      622
Cabibbo angle      469
Callan — Symanzik equation      634
Campbell — Hausdorff formula      62 336
Canonical anti-commutation relations      178 216
Canonical commutation relations      9 16
Canonical momentum      22 26 45
Canonical momentum, Dirac      215
Canonical momentum, fermions      173
Canonical momentum, vector      248
Canonical momentum, Weyl spinor      177
Canonical momentum, Yang — Mills theory with fermions      391
Canonical quantization      22—29
Canonical quantization, conserved quantities      43
Canonical representation      31
Canonical transformation      85
Cartan subalgebra      144 150
Cartan subalgebra, su(3)      439
Casimir operator      68 153
Cauchy characteristics      660
Causality      19 20
Center of energy law      66
Center of mass frame      124
Charge      51
Charge conjugation      70—72 209
Charge conjugation, Dirac fields      230—233
Charge conjugation, Weyl fields      170
Charge of complex field      52
Charge, eigenquark      470 518
Charge, eigenstate      51
Charged particle      52
Chern — Simons term      431 476
Chiral, covariant derivative      366
Chiral, current      425
Chiral, fermions      426

Chiral, flavor SU(3)      530
Chiral, SU(2) symmetry      501
Chiral, symmetry      426
Chiral, symmetry of QCD      475
Classical background      271
Classical Electromagnetism      249
Classical fermions      364 418
Classical limit      24 179
Classical mechanics      22
Cluster expansion      93
COLOR      438 465
Color, singlets      482
Color, symmetry      444—445
Commutative Lie algebra      144
Complete set of independent fields      250
Complete set of operators      21
Completeness relation, Dirac spinor      214
Completeness relation, polarization vector      251
Completeness relation, quantum mechanics      329
Completeness relation, Weyl spinor      176
Complex field      52
Complexification of a Lie algebra      149
Component (topology)      429
Composite operator      552
Compton scattering      259—261 587
Confinement scale      480 658
Confining      656
Conjugate momentum      see "Canonical momentum"
Conjugate representation      439 484
Conjugate representation, so(1, 3)      161
Connected Green functions      292
Connected Wick diagram      93
Connection one-form      263 385
Conservation law - multiplicative      73
Conserved current      46 59 180 217 391
Conserved quantity      43 46 59
Conserved quantity, action of      50 60
Conserved quantity, canonical quantization      43
Conserved quantity, quantum      49
Consistent anomaly      427
Constituent quarks      491
Contraction      85
Contraction, derived fields      256
Contraction, Dirac fields      218
Contraction, Fermi fields      186
Contraction, Weyl fields      187
Coulomb gauge      259
Coulomb potential      258
Counterterm Lagrangian      288
Counterterm Lagrangian, QED      566
Counterterm renormalization      593 603 632
Coupling renormalization condition      294 309
Covariance      340 343 359
Covariance, Bose fields      344
Covariance, Fermi fields      363
Covariance, matrix      357
Covariant anomaly      427
Covariant conservation      392 425
Covariant derivative      263 265 386 389 391
Covariant derivative, electroweak      458
Covariant derivative, hermitian      264
cp      241
CP, Standard Model      470
CP, strong interactions      475
CPT invariance      70
CPT invariance of amplitudes      116
CPT invariance of field theory      77
CPT on amplitudes      109
CPT on diagrams      108
CPT on Feynman integrals      242—244
Creation operator      16
Creation operator, Lorentz normalization      16
Creation operator, time-dependent      21
Creation operator, wave-packet      279—280 303 310
Cross section      130
Cross section, high-energy approximation      131
Crossing      114
Current algebra - axial current      558
Current conservation      266
Current octet matrix      487
Current quark      491
Curvature tensor      387
Dalitz Plot      126—128 526
de Broglie      662
Decay rate      128
Decay rate, deviation from exponential law      320
Decay rate, unstable particle      325
Decay width      128
Decay, $B \rightarrow B^{'}e\bar{\nu}_{e}$       525—530
Decay, $e^{-}e^{+} \rightarrow \mu^{-}\mu^{+}$       464
Decay, $K^{-} \rightarrow \pi^{0}e\bar{\nu}_{e}$       522
Decay, $\pi^{-} \rightarrow e^{-}\bar{\nu}_{e}$       516
Decay, $\pi^{-} \rightarrow \mu\bar{\nu}_{\mu}$       519
Decay, $\pi^{-} \rightarrow \pi^{0}e^{-}\bar{\nu}_{e}$       520
Decay, $\pi^{0} \rightarrow 2\gamma$       503—505
Decay, suppression factors      518
Decay, tauon      515
Degree of a representation      142
Delta functional      30 379
Delta functions - products of      107
Derivative interaction      119 255
Derivative interaction, Feynman rule      355
Diagonalization theorems      200—202
Differential cross section      129
Differential geometry      387
Differential transition probability      122
Dimensional regularization      544
Dimensional regularization, $\gamma_{5}$ and $\epsilon_{\mu\nu\rho\sigma}$       551
Dimensional regularization, axial current      558
Dimensional regularization, integral formulae      546
Dimensional regularization, mass parameter      545
Dimensional regularization, numerator substitutions      545
Dimensional transmutation      633
Dirac adjoint      203
Dirac adjoint of matrix      210
Dirac algebra      206 208
Dirac algebra, D dimensions      549—551
Dirac algebra, formulae      222—223
Dirac algebra, projections      211
Dirac algebra, representation      208—209
Dirac equation      206 207
Dirac field      203 215—221
Dirac field, renormalization      302—309
Dirac field, self energy      307
Dirac field, table of particles      218
Dirac magnetic moment      525 591
Dirac mass term      171 200 203
Dirac plane waves      212
Dirac polarization spinor      212
Dirac polarization spinor, completeness relations      214
Dirac polarization spinor, discrete symmetries      242
Dirac polarization spinor, normalization relations      214
Dirac polarization spinor, phase ambiguity      214
Dirac representation      208
Direct sum of Lie algebras      141
Direct sum of representations      142
Disconnected Feynman diagram      291
Disconnected Wick diagram      93
Discrete symmetries      70—78
Discrete symmetries, Dirac fields      230—244
Discrete symmetries, Fermi bilinears table      240
Discrete symmetries, photon field      267
Discrete symmetries, polarization-spinor phases      242
Distribution theory      184
Divergence, disjoint      603
Divergence, logarithmic      117
Divergence, nested      603
Divergence, overlapping      604
Dyson's formula      274
Effective interaction      608 621 623

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