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O'Raifeartaigh L. — Group Structure of Gauge Theories

O'Raifeartaigh L. — Group Structure of Gauge Theories

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Название: Group Structure of Gauge Theories

Автор: O'Raifeartaigh L.

Аннотация:

This monograph provides an account of the structure of gauge theories from a group theoretical point of view. The first part of the text is devoted to a review of those aspects of compact Lie groups (the Lie algebras, the representation theory, and the global structure) which are necessary for the application of group theory to the physics of particles and fields. The second part describes the way in which compact Lie groups are used to construct gauge theories. Models that describe the known fundamental interactions and the proposed unification of these interactions (grand unified theories) are considered in some detail. The book concludes with an up to date description of the group structure of spontaneous symmetry breakdown, which plays a vital role in these interactions. This book will be of interest to graduate students and to researchers in theoretical physics and applied mathematics, especially those interested in the applications of differential geometry and group theory in physics.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1986

Количество страниц: 184

Добавлена в каталог: 13.04.2008

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Предметный указатель

$S(U(2)\times U(3))$ theory      107—109
Abelian group      4
Abelian Higgs mechanism      96
Abelian Lie algebra      23
Additive quantum number      66 70
Adjoint group representation      20 142—145
Adjoint representation of algebra      25
Analytic S-matrix      101
Associativity      3 13
Asymptotic field      97—98
asymptotic freedom      72 84—87 101—102 119 120 125
Automorphism      5 6
Axial (ABJ) anomaly      82—84 108 117 119 121
B-L conservation      115 121
Baker — Campbell — Hausdorff formula      19
Baryon      66 73 101
Baryon-photon asymmetry      117
Beta-function (of renormalization group)      85
Bianchi identity      81
Bottom quark      71
Cabbibo angle      69 108 123
Canonical commutation relation      63 95
Cartan canonical form (of Lie algebra)      27—29 36
Cartan classes (of Lie algebra)      33—34
Cartan matrix      33 133—134
Cartan metric      24—26 60
Cartan subalgebra      28 91
Casimir operator      59—62 84 90
Centre (of group)      4 20 25 34 122
Centre (representation of)      52—56
Characters (Weyl formula)      38—39 58
Charm      71 108
Chirality      92 103
Classical group      11
Classification of particles      63 66—73 101—109
Clebsch — Gordon coefficient      64 110 134
Clifford algebra      45 48 57—58
Closed subgroup      9 89 129 135
Colour      72—73 101—102 134
Commutator      22
Compactness      26
Compactness (algebra)      7 9
Complex representation      56—58 118—122
Complexification (of algebra)      28
Composite field      101
Confinement of quarks      70 102
Conjugation      4 20
Connectivity      7—8
Connexion form      82
Conserved current, charge      65 106—107
Construction of HIRs      43 46
Coset      4 128
Cosmology      72 108 117 123—125 151
Covariant derivative      77—82 106
Covering group      11—12 52—54
Coxeter matrix      33
CP-violation      108 126
CUIRs      Chapter 5
Current algebra      70 101
Curvature      82
Decoupling theorem      111
Deep-inelastic scattering      101
Differential forms      16
Differential geometry      82
Dimensional regularization      103
Dimensions of representation      58—59
Dirac fields      64
Dirac matrices      21 45 48
Dominant weight      36—38
Double-covering (of SO(n))      34 42—47 53—58
Duality in Lie algebra      134
Dynamics      79 81
Dynkin diagrams      32—33 47—48
Dynkin indices      42 47 58—59
Effective coupling constant      85
Electric charge, current      67 77—78 96 104—105 125
Electromagnetism      77—78 101 103—107
Electroweak interaction      71 101 103—107 125
Elementary fields      66 73 126
Euclidean QFT      89
Euler angles      13 20
Euler — Lagrange field equations      65 81
Exceptional group GUT models      122
Fermi coupling constant      107
Fermi statistics (and colour)      72
fermions      64 91 104
Fibre-bundles      82
Fine-tuning      151—152
Finite dimensionality of representation      51
Flabour      66—73 102
Fractional charges      70
Functional integration      103
Gauge ambiguity      82
Gauge couplings      81—82
Gauge field      80
Gauge field (masses)      90—91 148
Gauge potential      79—80
Gauge principle      77—82 125
Gauge transformation      77—80
Gauge, choice of      96—98
Gauge-hierarchy problem      126 151—153
Gell-Mann — Okubo mass formula      68 74
Generations (of fundamental fermions)      72 108—110 126—127 118 123
Generic strata      135
GIM mechanism      108
Glueballs      103
Gluons      101—102
Goldstone theorem      92—93 124 145 148—149 150 152—153
Grand unification      Chapter 12
Grand unification models      113—124
Grand unification scale      111—113 116 149—152
Gravitation      101 153
Gupta — Bleuler mechanism      95—96
Hadrons      66 71
Heisenberg group      5
Hermitian representations of algebras      Chapter 4
Hierarchy problem      126 151—153
Higgs mechanism      16 95—98 99
Highest weight      37—38
Homomorphisms      5
Homotopy      8
Horizontal symmetry      118 122—124
Hypercharge      67
Idempotent      133—134
Identity component of group      7 8
Index of CUIR      60—61 86
Infinitesimal generators      15 49 51
instantons      83 126
Integrability conditions      14 15 49
Internal (symmetry) groups      63
Invariant subgroup      4
Invariants      137—142 (see also “Casimir operator”)
Isomorphism      6
Isoparity      67
Isospin      67
Isotropy group      89
Isotropy of invariants      137
Jacobi identity      15 18 24 25
Jets      103
Jordan algebra      34
Kernel      6 11
Kinetic terms      78 81
KM-matrix      108—109 118 123
Lagrangian      64 70 77 79 90 96
Lagrangian (electroweak)      106
Lagrangian (strong)      101—102
Lagrangian (SU(5))      115
Landau gauge      91
Landau — Ginsburg superconductivity      96 126
Lattice gauge theory      103

Leptons      66 71—73 104—105 110
Levi-Civita invariant      61 64
Lie algebra      13 18 Chapter
Lie algebra (representations)      Chapter 4
Lie groups, general      10—12
Lie groups, general (local properties)      Chapter 2
Lie groups, general (representations)      Chapter 4
Linear representation      50
Little group      89 90 93 Chapters 12
Lorentz group      64
magnetic moment      68
Magnetic monopole      134
Mass      102 122 142—149
Mass (fermion)      92
Mass (gauge field)      90—91
Mass (quark)      70—72
Mass (renormalization group)      111
Mass (scalar field)      94—95
Mass (W, Z)      107
Mass formulae      68 69 71 74
Maximal compact subalgebra      35
Maximal little group      129
Maximal orbit      135 141
Maxwell Lagrangian      77
Measure (group)      8 9 16 21
Meissner effect      88
Mesons      66 73 88
Metastable hadrons      67
Metric (Cartan)      24—26 60
Metric (group)      9 16 21
Michel conjecture      141
Minimal little group      129 135
Minimal principle      77
Models of unified gauge theory      113—124
Modular factor      9
Monomial invariant      137
Montgomery — Zippen theorem      14 20
Mostow theorem      135 141
N-ality      53—54
Neutral current      104 107 118 122
Neutron      67
Noether current, charge      65—67 74 78 98 115 116
Non-abelian Higgs mechanism      97—98
Non-compact semi-simple algebra      35
Non-gravitational interaction      101—109
Normal parameter      17—19
Octonions      34
Orbital excitations (of quarks)      69
Orbits      3 89 128—141
Ordering of little groups, spaces      135—136
Ordering of roots      32
Orthogonal group      10 11 34 43 45—46 53—54 57 130 117 121—124
Orthogonality of representations      51
Parameter transformations      17 19
Parity      68 103
Pauli matrices      11 45 48 57 64 67 104—108 130
Peccei — Quinn symmetry      124—125
Peter — Weyl theorem      51
Physical gauge      91 97—98
Planck mass      113 125
Poincare group      64 79
Poisson bracket      22 66
Polar field      94 153
Potential      64 88—95 106 120 126 128 Chapter
Primitive representations      42—44 84 113 124
Primitive root      32
Primitive weight      40
Product (direct, semi-direct)      6 8
Proton      67
Proton decay      110 113 116 121 127 134
Pseudo-Goldstone field      93
Pseudo-real representations      56—58
Quantization condition (roots)      30
Quantization condition (weights)      37
Quantum chromodynamics (QCD)      101—103
Quantum field theory (QFT)      89
Quark confinement      70 102
Quark mass      70—72 102
Quark-lepton symmetry      84 108
Quarks      67 69—73 101—103 110
Quaternions      34 130
Quotient group      5 6 56
Rank index (of representation)      53—54
Rank of Lie algebra      28 136
Reality of representations      56—57 117—119
Renormalization      79 84 88 90 103 140
Renormalization group equation      85—87 110—112
Representation of group centre      53—56
Representations of compact Lie algebras      Chapter 4
Representations of compact Lie groups      Chapter 5
Residual symmetry group      89
Rigid (symmetry) group      63 77—79
Root diagram      30—32
Rules for GUT models      118—120
S-matrix      101
Safe groups, representations      84
Semi-simple algebra, group      23—25 27 123
Simple connectivity      8 11
Simple group GUT-models      121
Simple group, algebra      23—25 27—35
SO(10) GUT model      117
SO(n) groups      10 11 34 43 45—46 53—54 57 117 121—124 130
Spinor representations      42 45—48 117 119
Spontaneous symmetry breaking      Chapters 8 10 12
Stability subgroups      89
Standard electro weak model      103—107
Strange quarks      70
Strata      128—132 135—136
String theory      123
Strong interactions      70
Structure constants      15 18 19 24 26 29—32 60
Structure functions      13—19
Structure theorem for compact Lie algebras      27
SU(2) orbits      129—130
SU(5) GUT model      113—117
SU(N)      23 34 43—44 53—56 59 84 86 119 121 123—124 131—134 137 142—149
Subalgebras      22 23
Subgroups      4
Sum (direct, semi-direct)      23
Superconductivity      96 126
Supersymmetry      123 126 152—153
Symmetric algebra      132—134
Symmetric tensor representation      130—131 134 136—137 142—144
Symmetry group      3 63
Table of Casimirs, indices      61
Table of electroweak U(2) assignments      105
Table of roots, primitive roots, weights      41
Tangent matrix      14 15—21
Technicolour      124—125
Tensor representations      42—44 131—134
TeV experiments      127
Theta-vacua      126
Top quark      71 118
Topological charge      83 134
Topology of coset      128—129
Topology of group      7—9
Triality      53—54 69
True group      52—56
Unified gauge theory (UGT)      Chapters 7 9
Unitarity of representations      50
Unitary groups      11 23 34 53—56 77 Chapter
Unitary trick      35
Vectorlike assignment      84
W and Z mesons      71 88 103—104 107
Weak angle      104 106 112 118 122
Weak hypercharge      105
Weak interactions      68—69 101 103—107
Weight diagrams      36—38
Weyl character formula      38—39 58
Weyl field      64

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