Bailin D., Love A. — Introduction to Gauge Field Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Bailin D., Love A. — Introduction to Gauge Field Theory

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Название: Introduction to Gauge Field Theory

Авторы: Bailin D., Love A.

Аннотация:

Introduction to Gauge Field Theory provides comprehensive coverage of modern relativistic quantum field theory, emphasizing the details of actual calculations rather than the phenomenology of the applications. Forming a foundation in the subject, the book assumes knowledge of relativistic quantum mechanics, but not of quantum field theory. The book is ideal for graduate students, advanced undergraduates, and researchers in the field of particle physics.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 384

Добавлена в каталог: 08.11.2008

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Предметный указатель

$R_{\xi}$ gauge      183—184 186
$SU(2)\times U(1)$ invariance      233
Abelian gauge field theory      110—111
Angular momentum tensor      23 26 30 37
Annihilation operators      39
anomalies      272
Anomalous dimensions      158—162
Anomalous magnetic moment, of electron      140—142
Asymmetric phase      338 340—341 343
Asymptotic behaviour      54—55
Asymptotic conditions      55
asymptotic freedom      147
Axial gauges      125 130
Axial U(1) symmetry      218
Axial vector current conservation      217
Axion      217
Axion, invisible      226
Axion, mass      225—256
Bare coupling constant      75
Bare Lagrangian, for gauge theory      132
Bare mass      75
Baryon number conservation      40
Baryon number violation, by colour triplet Higgs scalars      309
Bjorken limit      151
Bjorken scaling      155
Bottom quark mass, in grand unified theory      313
Boundary conditions, for path integrals      40—41
BRS transformations      346
Charge      19
Chiral theory      273
Chiral transformation      38
Chirality      191
Classical field      15 47 174
Classical field, as solution of the classical field equation      48
Classical field, relation to vacuum expectation value of field      47
Closed fermion loops      135
Coleman — Weinberg mechanism      212
Coleman — Weinberg transition      342
Colour      116
Complex scalar field theory      24 175
Conjugate momentum, in field theory      39
Connected Green functions      46
Connected Green functions, in momentum space      47
Conserved current      18—20
Continuation to Euclidean space, of vacuum amplitude      41
Continuation to imaginary time, for ground state amplitude      10—11
Counter term, Lagrangian      85
Counter terms      263
Counter terms for gauge theories      132
Covariant cut-off      79
Covariant derivative      185
Covariant derivative for Abelian gauge field      111
Covariant derivative for non-Abelian gauge fields      112 115 125
Covariant spin vector      27 33
Creation operators      39
Critical temperature      336 338—340
Curie temperature      172
Deep inelastic scattering      149 162
Deep inelastic scattering, moments of structure functions      162—163
Deep inelastic scattering, structure functions      150
Degree of divergence      77
Degree of divergence for Feynman diagrams with fermions      101—103
Degree of divergence for gauge theories      131
Derivative interactions      103
Derrick's theorem      194
Dilatation      37 38
Dimensional regularisation      79—81
Dimensional transmutation      212
Diquarks      301 303
Diquarks, masses      309
Dirac $\delta$ function, integral representation      44
Dirac equation      25
Dirac field      31
Dirac matrix identities, in $2\omega$ dimensions      137 139
Divergences      17
Effective action      48 201—203
Effective action for free scalar field      48
Effective potential      49 200—212
Effective potential at finite temperature      313—318
Effective potential, expansion in terms of Green functions      50
Eigenstates, of the field operator      39
electric dipole moment      220
Electromagnetic current      31 216 218
Electron-positron annihilation, inclusive process      165—167
Electroweak theory      214 232
Electroweak theory at finite temperature      322—323
Energy-momentum tensor      23 35
Energy-momentum vector      22 27 35
Euclidean space, continuation of Feynman propagator      44
Euclidean space, continuation of vacuum amplitude      41
Euclidean space, Green functions      41
Euler — Lagrange equations      16—17 26 34 170
Faddeev — Popov ghosts      123—125
Faddeev — Popov Lagrangian      187 189
Faddeev — Popov procedure      119—123
Fermi coupling constant      214
Fermi statistics, at finite temperature      306
Fermion loops      105—106
Fermion mass matrix      190 192
Fermion mass terms      217
Fermion masses in electroweak theory      223 233
Fermion masses in grand unifield theory      294—297
Fermionic functional integration measure      273
Ferromagnet      172
Feynman diagrams      62—63
Feynman diagrams for free scalar field theory      45
Feynman gauge      126 140 261
Feynman integrals      81—85
Feynman integrals in $2\omega$ dimensions      329
Feynman parameter      82—83 141
Feynman propagator for Dirac field      100
Feynman propagator for Faddeev — Popov ghosts      126
Feynman propagator for scalar field theory      43—44
Feynman propagator in momentum space for Dirac field      101 128
Feynman propagator in momentum space for scalar field theory      44
Feynman propagator, diagramatic representation of scalar propagator      46
Feynman rules      63 187
Feynman rules for $\lambda{\o}^4$ theory      60
Feynman rules for electroweak counter terms      248—258
Feynman rules for electroweak gauge boson vertices      224—231
Feynman rules for electroweak gauge bosons      221 225—226
Feynman rules for electroweak ghost particles      222 224
Feynman rules for electroweak Goldstone bosons      222 226 228
Feynman rules for electroweak Higgs particle      222 226 228
Feynman rules for Faddeev — Popov ghosts      126 128
Feynman rules for fermion antiparticles      107—108
Feynman rules for fermion loops      105—106
Feynman rules for fermion propagators      104
Feynman rules for fermion-fermion scattering      107—108
Feynman rules for gauge field interactions      127—129
Feynman rules for momentum space      64
Feynman rules for quarks in electroweak theory      238 240
Feynman rules for S-matrix elements      70
Feynman rules for temperature Green functions      312
Feynman rules for Yukawa interactions      103—106
Feynman rules from counter terms      86
Field equations, for gauge field theories      114
Fine structure constant      142 232
Finite temperature effective potential      313—314
Finite temperature effective potential at one loop order      314—319 321 323
Free energy      315
Functional derivatives      3 13 40—41 48 122
Functional derivatives for fermions      99
Functional derivatives with respect to spinor sources      104
Functional expansion in terms of connected Green functions      46
Functional expansion in terms of Green functions      41
Functional expansion in terms of opi Green functions      48
Functional expansion of effective action      48
Functional expansion of vacuum amplitude      41
Gauge boson mass matrix      186

Gauge invariance      170
Gauge invariance, Abelian      110
Gauge invariance, non-Abelian      113—114
Gauge invariant Lagrangian for Abelian gauge field      111
Gauge invariant Lagrangian for non-Abelian gauge fields      114
Gauge invariant Lagrangian of renormalised Lagrangian      131
Gauge parameter ( $\xi$ )      289 346
Gauge transformation      24 30 34
Gauge-fixing Lagrangian      183 186
Gauge-fixing term      34 121 124—125
Gaussian integral      1
Gaussian integral for Grassmann variables      96—99
Gell-Mann $\lambda$ matrices, normalisation      299
Generating functional for connected Green functions      46
Generating functional for Euclidean Green functions      41
Generating functional for Gauge theories      123—125
Generating functional for Green functions      40—41
Generating functional for spinor field theories      99
Generating functional in free scalar field theory      42—45
Global transformation      19 24 30
Goldstone boson      177 179—180 183 185 187—188 218 224
Goldstone modes      220 222
Gordon reduction      142
Grand unification scale      298 305—306
Grand unified theory      198 225 298
Grassmann variables      28—29 96 210
Grassmann variables, complex      98 123—124
Green functions      40
Green functions for Faddeev — Popov ghosts      136
Green functions for free scalar field theory      45—47
Green functions for gauge fields      133—135
Green functions for opi      66
Green functions for spinor field theories      99
Green functions high momentum behaviour      149
Green functions in Euclidean space      41
Green functions in momentum space      46
Green functions, connected      46
Green functions, inserted      157
Green functions, one-particle-irreducible      47—50
Green functions, unrenormalised      144
Ground state expectation values in quantum mechanics      11—14
Ground state expectation values in terms of ground state amplitude      14
Ground-state-to-ground-state amplitude, in quantum mechanics      8—11
Group generators, normalisation      114
Group theory factors      135 137 139
Group theory factors in renormalisation group equation      146
Hadronic weak current      252
Hamiltonian      22
Hamiltonian density      22 39 41
Heisenberg picture      5
Helicity      31 33 37
Higgs field      174 183 187—189 209
Higgs mechanism      180
Higgs mechanism in non-Abelian theories      185
Higgs model      180 207
Higgs model at finite temperature      334—336 340
Higgs scalar      337
Higgs scalar for electroweak breaking      309
Higgs scalar mass      342
Higgs scalar potential for SU(5) breaking      308
Higgs scalar, breaking SU(5) symmetry      307—308
Identical fermions, factors in scattering amplitudes      108
In and out fields      54—55
Infinities      75 79
Infrared divergence      83 139 142
instantons      212—213
Invariant amplitude, for fermion-fermion scattering      108
Klein — Gordon equation      21
Lagrange multiplier      34
Lagrange's equations      16
Lagrangian      15
Lagrangian density      15 41
Landau gauge      126 148—149 208 210
Lepto-quarks      301 303
Lepto-quarks, masses      309
Leptonic current      330
Light cone      152—153
Light cone coordinates      151—152
local gauge invariance      34 79
Logarithmic divergence      77
Loop expansion      201 207
Lorentz (gauge) condition      34—35 170 183
Lorentz transformation      23
Magnetic charge      200
Magnetic monopoles      193—200
Magnetisation      172
Mass-independent renormalisation schemes      91
Massless fermions, generating functional      106
Massless fermions, propagators      107
Matsubara frequencies for bosons      318
Matsubara frequencies for fermions      323
Maxwell's equations      17 33
Minimal subtraction (MS)      90 206
Minimal subtraction (MS) in gauge theory      133
Minimal subtraction (MS), MS scheme      91 206
Momentum scheme      92
Muon decay      249—252 285
Noether current      25 31 178
Noether's theorem      18—19
Non-Abelian gauge field theory      112—115
Non-abelian gauge symmetry      177
Non-Abelian gauge transformations      112—113
Normalisation factor, for generating, functional      42
On-mass-shell electrons      141
On-shell scheme      93
One-particle-irreducibility, of Green functions      47—50
Operator product expansion      152—153
Optical theorem      151
Parity      31 190—191
Partition function      315
Partition function as a path integral      317
Partition function for fermions      322—324
Partition function for free scalar field      317—320
Partition function for gauge adds      320—322
Path integrals for Grassmann variables      96—99
Path integrals for Grassmann variables in Minkowski space      98—100
Path integrals, Gaussian      1—4
Path integrals, over conjugate momentum      42
Peccei Quinn symmetry      223—224
Perturbation series, with fermions      104
Perturbation theory      60
Phase transformation      110
Phase transition, first order      339—341
Phase transition, second order      336
Physical renormalisation      206
Poincare transformation      21 27
Polarisation vectors of a massive vector field      171
Polarisation vectors, longitudinal      171
Pontryagin index      213—214
Prasad — Sommerfield solution      197
Projection operators, for gauge field propagators      117—118 126
Proton decay      309 313
Quadratic divergence      77
Quadratic divergence in gauge theory      133
Quantum chromodynamics (QCD)      116 192
quantum mechanics      51
Quarks      236
Radiative corrections to muon decay      285—288
Renormalisable field theory      75 169
Renormalisable interactions of fermions with scalars      102
Renormalisation      74—78
Renormalisation group coefficients      145—146
Renormalisation group equation      145
Renormalisation group equation for Wilson coefficients      157—158
Renormalisation group equation, solution of      146—147
Renormalisation scheme      88 90 260
Renormalisation, of $\lambda{\o}^4$ theory      74—78 85
Renormalised coupling constant      74
Renormalised field      75 85
Renormalised Lagrangian, for gauge theories      131

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