Aitchison I.J.R. — An Informal Introduction to Gauge Field Theories :: Электронная библиотека попечительского совета мехмата МГУ

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Aitchison I.J.R. — An Informal Introduction to Gauge Field Theories

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Название: An Informal Introduction to Gauge Field Theories

Автор: Aitchison I.J.R.

Аннотация:

Four forces are dominant in physics: gravity, electromagnetism and the weak and strong nuclear forces. Quantum electrodynamics - the highly successful theory of the electromagnetic interaction - is a gauge field theory, and it is now believed that the weak and strong forces also can be described by generalizations of this type of theory. In this short book Dr Aitchison gives an introduction to these theories, a knowledge of which is essential in understanding modern particle physics. With the assumption that the reader is already familiar with the rudiments of quantum field theory and Feynman graphs, his aim has been to provide a coherent, self-contained and yet elementary account of the theoretical principles and physical ideas behind gauge field theories.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 174

Добавлена в каталог: 09.12.2009

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Предметный указатель

$J/\psi$ particles      119 121
$\beta$ -function      162—163
$\eta$ decay      155
$\eta$ mass      155
$\nu-e$ scattering      110—112
$\nu-e$ scattering, inelastic      120
$\pi^{0}$ decay      148—155
$\sigma$ -model      94—95 114
$\tau$ lepton      121
$\theta$ parameter      38 121
't Hooft gauge fixing term(s)      66 99 104
Action principle      10
Adler — Weissberger relation      95 147
Algebra Lie of charges      24 92 95
Algebra Lie of currents      24 95
Algebra Lie of generators of group      20 34
Algebra Lie, matrix representation of      20 92
And departures from scaling      163
Anomalous dimension      158 162
Anomaly      16 126 148 153 160
Anomaly and $\eta$ mass      155
Anomaly and renormalisation      154
Anomaly and scale invariance      155—163
Anomaly and U(1) problems      155
Anomaly, $\gamma_{s}$       148—155 160
Anomaly, cancellation      155
Anomaly, cancellation in GSW theory      154—155
asymptotic freedom      2 122 162
Auxiliary field      45—47 56
Axial vector, charge      92
Axial vector, current      92 94
Axial vector, current and anomalies      148—155
Axial vector, current and Ward — Takahashi identities      146—147
Axial vector, current, non-conservation of      94 146
Axial vector, current, partial conservation of (PCAC)      94
Baryon, decay      123
Baryon, number conservation      124
Becchi — Rouet — Stora (BRS) transformation, Abelian      54—55
Becchi — Rouet — Stora (BRS) transformation, non-Abelian      54—56 147
Bogoliubov, quasiparticle operators      80—81
Bogoliubov, superfluid      79—83
Bogoliubov, transformation      82
Born graphs, high energy behaviour of      63—64 68 99 106
Bose condensate      79 82 83
BSC theory of superconductivity      83
Cabibbo, angle      115 144
Cabibbo, angle, generalised      121
Cabibbo, mixing      5
Callan — Treiman relation      95
Charge, algebra      24 95
Charge, axial vector      92
Charge, conserved, associated with symmetry      13—14 16 19—22
Charge, quantisation      36 124 144
Charge, renormalisation      137
Charge, renormalisation and vacuum polarisation      144
Charge, renormalised      137 144
Charge, unrenormalised      136—137 144
Charge, weak      5 145
Charged current      3 5
Charm      117 118
Charm-changing decays, selection rules in      118—119
Charmed mesons      118—119
Charmed mesons, mass prediction (GIM)      119
Chiral symmetry      2 71
Chiral symmetry and $\eta$ mass      155
Chiral symmetry and $\pi^{0}$ decay      148—155
Chiral symmetry and anomalies      148 149—153
Chiral symmetry, hidden global      91—96 146
Colour      1 37
Colour and $\pi^{0}$ decay      153
Colour, group $SU(3)_{c}$       2
Commutation relations in canonical quantisation      12
Condensate (Bose)      79 82 83
Condensate (Bose), Cooper pair      100—101
confinement      163
Conservation law and anomalies      15—16
Conservation law and symmetry      13 16 19
Cooper pairs      100
Cooper pairs, wavefunction of      101
Correlation length in statistical mechanics      156 162
Coulomb interaction, instantaneous      57
Coulomb interaction, instantaneous in spontaneously broken theory      78—79 81
Coulomb interaction, instantaneous in superconductor      83
Coulomb interaction, instantaneous, modified by renormalisation      136
Counter terms      129—131 134 137—138 141 146 148
Covariant derivative, $SU(2)\times U(l)$       101 108—109
Covariant derivative, general      34
Covariant derivative, QED      25 31
Covariant derivative, regular representation      35 46
Covariant derivative, SU(2) doublet      32
Covariant derivative, SU(3) triplet      38
CP violation      120—121
Critical indices      162
Critical phenomena      162
Critical temperature      87 156
Curie temperature      76 85
Current as source in gauge theories      27 36
Current in vacuum      100
Current, algebra      24 95 146
Current, associated with spontaneously broken global symmetry      87 99
Current, associated with spontaneously broken local symmetry      99—100
Current, axial vector      92 94
Current, conservation and Ward identity      50 140—144
Current, conserved weak vector (CVC)      145
Current, conserved, associated with symmetry      14—19 21—24 27 71 73
Current, conserved, associated with symmetry and Coleman's theorem      72
Current, electromagnetic      27
Current, electromagnetic and gauge invariance      27
Current, hadronic weak      4 114—120
Current, leptonic      4
Current, screening      100
Current, weak for quarks      115
Current, weak neutral, strangeness changing      115
Current, weak neutral, strangeness changing and GIM mechanism      115—120
Current, weak vector      4 94 144—145
Current-current interaction      4 5
Cut-off      127—129 159—160
Deep inelastic lepton scattering and scale invariance      155—156 163
Degenerate ground states      75—77 82
Degenerate vacua      71
Dimension, anomalous      158 162
Dimension, scale      158
Dimensional analysis      156—157 162
Dimensional regularisation      127 133
Dimensional rescaling      157
Divergences, infra-red      127 139 148 160
Divergences, ultraviolet      6 15 64 126
Divergences, ultraviolet in $\pi^{0}$ decay      152
Effective charge      129
effective mass      128
Einstein      7—9
Equivalence, principle of      7
Euclidean region      160
Euler — Lagrange equations      10—11
Fabri — Picasso theorem      71—73
Fermi constant      110 114
Fermi theory      3 6
Fermion masses      38 93—95 113—114 120
Ferromagnet      75—78 85
Feynman gauge      44—45 48 57 64 67 127 133 135 139
Field tensor in QCD      38
Field tensor, electromagnetic      26 33 40
Field tensor, non-Abelian      33—35
Flavour      1 37 94 115 120—121
Flavour, octet of weak currents      115—116
Four-fermion theory, connection with GSW theory      110
Gap in electron energy spectrum in superconductor      83
Gauge fields, quantisation of      39—57
Gauge independence of physical amplitudes      148
Gauge invariance and local phase transformation      8 25 28—29 31

Gauge invariance and mass of vector quanta      6—7 29—30 36—37 58—59
Gauge invariance and renormalisability      6 30 98
Gauge invariance in QED      2 26—29
Gauge invariance, hidden      5 7 9 30 36 58—59 96—104
Gauge invariance, non-Abelian      2 30—38
Gauge parameter      45—46 65 67—68 139
Gauge parameter, renormalisation of      139
Gauge principle      28—30 83 96
Gauge transformation in QED      26 28—29
Gauge transformation in Stuckelberg formalism      66 68—69
Gauge transformation, non-Abelian      30—33
Gauge, axial      57
Gauge, Coulomb      39 57
Gauge, covariant      46
Gauge, Feynman      44—45 48 57 64 67 127 133 135 139
Gauge, Landau      45
Gauge, Lorentz      39—40
Gauge, planar      57
Gauge, R      99 148
Gauge, U      99 104 148
Gauge-fixing term      38 45—46 57 65—66 113
Gauge-fixing term, 't Hooft      99 104
Gauge-fixing term, absence of counter-term for      139
Generations      107 120—121
Generator of $SU/(2)\times U(l)$       88
Generator of symmetry transformation      14—17 19—20 34
Georgi — Glashow electroweak model      63
Georgi — Glashow SU(5)      121—124
Ghosts      38 53 55—57 63 147
Glashow — Iliopoulos — Maiani (GIM) mechanism      117—118
Glashow — Salam — Weinberg (GSW) theory      1 30—31 36 58 60 62—63 70—71 87 90 105—124 145 154
Glashow — Salam — Weinberg (GSW) theory, connection with four-fermion theory      110
Global invariance      23 33
Global symmetry      71 83 85 87
Global transformation      8 23 31 69
Gluon      2 38
Gluon, exchange      2
Goldberger — Treiman relation      95
Goldstone, boson (massless modes in hidden symmetry)      73—83 86 88—89 93 96—97 99 139 155
Goldstone, boson (massless modes in hidden symmetry), 'swallowed' (in hidden gauge symmetry)      90
Goldstone, model      83—87
Goldstone, model, electromagnetic interactions in (Higgs model)      96—101
Goldstone, state      87
Goldstone, theorem      73 76—77
Grand unification      120—124
Gravity      7—9
Heisenberg interaction      76
Helmholtz free energy      84—85
Higgs, boson      98 103
Higgs, field      97 101 104 106
Higgs, field, mass      103 114
Higgs, mechanism      145
Higgs, meson      63
Higgs, model      96—101
Higgs, potential      121
Hypercharge, strong      37
Hypercharge, weak      106
Improper graphs      128
Inelastic electron scattering      120 155
Inelastic neutrino scattering      120 155
Invariance and conserved charge operators      20
Invariance, global      23 33
Invariance, local      23 33
Isospin and SU(2) group      28 33 89 94 102
Isospin, currents      94 145 147
Isospin, hadronic      22 30 37 94—95 115 145
Isospin, left-handed      92
Isospin, right-handed      92
Isospin, weak      30 94 105—106
IVB      109
Kibble model      78—79
Klein — Gordon equation      11
Landau mean field theory      85
Lepton mass      109 113—114
Lepton number      124
Lie algebra      20
Little group      89
Local invariance      23 33 145
Local non-Abelian symmetry      30—36
Local transformation      8 23 28 31 69
London equation      100
Loops and unitarity in non-Abelian gauge theories      52—53 56—57
Loops and unitarity in QED      55
Lorentz, condition      39 42—43 49
Lorentz, force      25
Lorentz, gauge      39—40
Low energy theorems      145—147
Mass of vector quanta and gauge invariance      7 29—30 36 105
Mass of vector quanta and renormalisability      7 58 68
Mass of vector quanta in GSW theory      110
Mass of vector quanta in hidden symmetry      83 98—104
Mass shift, due to renormalisation      128 130 138
Mass, unrenormalised      133
Massless states and hidden symmetry      74 76—77 79 81 85
Massless theories and scale invariance      156—158
Meissner effect      100
Minimal interaction in QED      25 29 31
Minimal interaction in Stuckelberg formalism      69
Momentum, canonically conjugate      11
Momentum, canonically conjugate to A°      41 45 57
Nambu — Goldstone realisation (of symmetry)      71
Nambu — Goldstone realisation of chiral symmetry      91 94 146
Negative norm states      39 42 67
Negative norm states, cancellation: in massive vector theory      68
Negative norm states, cancellation: in QED      44 68
Neutral weak current      3—5 63 105 109—112 115—120
Noether current      22 27 36 71 73 115
Noether current and BRS symmetry      56
Noether current and scale invariance      159
Noether's theorem      14 28
Non-Abelian gauge theories      2 30—38
Non-Abelian gauge theories and asymptotic freedom      162
Non-Abelian gauge theories, Feynman rules      39
Non-Abelian gauge theories, renormalisability      6 30
Non-Abelian symmetry      20
Non-Abelian symmetry, hidden global      87—91
Non-Abelian symmetry, hidden local      101—104
Non-Abelian symmetry, manifest local      29—36
Non-renormalisable theories      6 58 125
On-shell particle      128
One loop renormalisation      137—138
One particle irreducible graphs      128
One particle irreducible Green functions      160
One particle reducible graphs      128
Order parameter      77
Parity violation      4
Parity violation in $e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}$       112—113
Parity violation in atomic physics      120
Parity violation in e-d scattering      120
Parity violation in electroweak interactions of hadrons      120
Parton model      115 120 163
PC AC      94—95 105
Penetration length      100
Phase angle, oscillations in      86 97
Phase transformation      8
Phase transformation, global      23 28 31
Phase transformation, local      23 25—26 28—36
Phase transformation, SU(2), SU(3)      8
Phase transformation, U(1)      8
Phase transition and hidden symmetry      85 87
Phase transition, Landau mean field theory of      85
Phase, hidden symmetry      101
Phonon-like modes in superfluid      81
Photon, mass      136
Photon, mass and hidden gauge symmetry      139
Photon, mass and infra-red divergences      139
Photon, polarisation vectors      42—43
Pion as Goldstone boson      94—95 146
Plasma frequency      82
Plasmons      82

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