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O'Raifeartaigh L. Ч Group Structure of Gauge Theories
O'Raifeartaigh L. Ч Group Structure of Gauge Theories

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Ќазвание: Group Structure of Gauge Theories

јвтор: O'Raifeartaigh L.

јннотаци€:

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.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1986

 оличество страниц: 184

ƒобавлена в каталог: 13.04.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$S(U(2)\times U(3))$ theory      107Ч109
Abelian group      4
Abelian Higgs mechanism      96
Abelian Lie algebra      23
Additive quantum number      66 70
Adjoint group representation      20 142Ч145
Adjoint representation of algebra      25
Analytic S-matrix      101
angular momentum      13
Associativity      3 13
Asymptotic field      97Ч98
asymptotic freedom      72 84Ч87 101Ч102 119 120 125
Automorphism      5 6
Axial (ABJ) anomaly      82Ч84 108 117 119 121
B-L conservation      115 121
Baker Ч Campbell Ч 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)      27Ч29 36
Cartan classes (of Lie algebra)      33Ч34
Cartan matrix      33 133Ч134
Cartan metric      24Ч26 60
Cartan subalgebra      28 91
Casimir operator      59Ч62 84 90
Centre (of group)      4 20 25 34 122
Centre (representation of)      52Ч56
Characters (Weyl formula)      38Ч39 58
Charm      71 108
Chirality      92 103
Classical group      11
Classification of particles      63 66Ч73 101Ч109
Clebsch Ч Gordon coefficient      64 110 134
Clifford algebra      45 48 57Ч58
Closed subgroup      9 89 129 135
Colour      72Ч73 101Ч102 134
Commutator      22
Compactness      26
Compactness (algebra)      7 9
Complex representation      56Ч58 118Ч122
Complexification (of algebra)      28
Composite field      101
Confinement of quarks      70 102
Conjugation      4 20
Connectivity      7Ч8
Connexion form      82
Conserved current, charge      65 106Ч107
Construction of HIRs      43 46
Coset      4 128
Cosmology      72 108 117 123Ч125 151
Covariant derivative      77Ч82 106
Covering group      11Ч12 52Ч54
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      58Ч59
Dirac fields      64
Dirac matrices      21 45 48
Dominant weight      36Ч38
Double-covering (of SO(n))      34 42Ч47 53Ч58
Duality in Lie algebra      134
Dynamics      79 81
Dynkin diagrams      32Ч33 47Ч48
Dynkin indices      42 47 58Ч59
Effective coupling constant      85
Electric charge, current      67 77Ч78 96 104Ч105 125
Electromagnetism      77Ч78 101 103Ч107
Electroweak interaction      71 101 103Ч107 125
Elementary fields      66 73 126
Euclidean QFT      89
Euler angles      13 20
Euler Ч 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      151Ч152
Finite dimensionality of representation      51
Flabour      66Ч73 102
Fractional charges      70
Functional integration      103
Gauge ambiguity      82
Gauge couplings      81Ч82
Gauge field      80
Gauge field (masses)      90Ч91 148
Gauge potential      79Ч80
Gauge principle      77Ч82 125
Gauge transformation      77Ч80
Gauge, choice of      96Ч98
Gauge-hierarchy problem      126 151Ч153
Gell-Mann Ч Okubo mass formula      68 74
Generations (of fundamental fermions)      72 108Ч110 126Ч127 118 123
Generic strata      135
GIM mechanism      108
Glueballs      103
Gluons      101Ч102
Goldstone theorem      92Ч93 124 145 148Ч149 150 152Ч153
Grand unification      Chapter 12
Grand unification models      113Ч124
Grand unification scale      111Ч113 116 149Ч152
Gravitation      101 153
Gupta Ч Bleuler mechanism      95Ч96
Hadrons      66 71
Heisenberg group      5
Hermitian representations of algebras      Chapter 4
Hierarchy problem      126 151Ч153
Higgs mechanism      16 95Ч98 99
Highest weight      37Ч38
Homomorphisms      5
Homotopy      8
Horizontal symmetry      118 122Ч124
Hypercharge      67
Idempotent      133Ч134
Identity component of group      7 8
Index of CUIR      60Ч61 86
Infinitesimal generators      15 49 51
instantons      83 126
Integrability conditions      14 15 49
Internal (symmetry) groups      63
Invariant subgroup      4
Invariants      137Ч142 (see also УCasimir operatorФ)
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      108Ч109 118 123
Lagrangian      64 70 77 79 90 96
Lagrangian (electroweak)      106
Lagrangian (strong)      101Ч102
Lagrangian (SU(5))      115
Landau gauge      91
Landau Ч Ginsburg superconductivity      96 126
Lattice gauge theory      103
Leptons      66 71Ч73 104Ч105 110
Levi-Civita invariant      61 64
Lie algebra      13 18 Chapter
Lie algebra (representations)      Chapter 4
Lie groups, general      10Ч12
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 142Ч149
Mass (fermion)      92
Mass (gauge field)      90Ч91
Mass (quark)      70Ч72
Mass (renormalization group)      111
Mass (scalar field)      94Ч95
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)      24Ч26 60
Metric (group)      9 16 21
Michel conjecture      141
Minimal little group      129 135
Minimal principle      77
Models of unified gauge theory      113Ч124
Modular factor      9
Monomial invariant      137
Montgomery Ч Zippen theorem      14 20
Mostow theorem      135 141
N-ality      53Ч54
Neutral current      104 107 118 122
Neutron      67
Noether current, charge      65Ч67 74 78 98 115 116
Non-abelian Higgs mechanism      97Ч98
Non-compact semi-simple algebra      35
Non-gravitational interaction      101Ч109
Normal parameter      17Ч19
Octonions      34
Orbital excitations (of quarks)      69
Orbits      3 89 128Ч141
Ordering of little groups, spaces      135Ч136
Ordering of roots      32
Orthogonal group      10 11 34 43 45Ч46 53Ч54 57 130 117 121Ч124
Orthogonality of representations      51
Parameter transformations      17 19
Parity      68 103
Pauli matrices      11 45 48 57 64 67 104Ч108 130
Peccei Ч Quinn symmetry      124Ч125
Peter Ч Weyl theorem      51
Physical gauge      91 97Ч98
Planck mass      113 125
Poincare group      64 79
Poisson bracket      22 66
Polar field      94 153
Potential      64 88Ч95 106 120 126 128 Chapter
Primitive representations      42Ч44 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      56Ч58
Quantization condition (roots)      30
Quantization condition (weights)      37
Quantum chromodynamics (QCD)      101Ч103
Quantum field theory (QFT)      89
Quark confinement      70 102
Quark mass      70Ч72 102
Quark-lepton symmetry      84 108
Quarks      67 69Ч73 101Ч103 110
Quaternions      34 130
Quotient group      5 6 56
Rank index (of representation)      53Ч54
Rank of Lie algebra      28 136
Reality of representations      56Ч57 117Ч119
Renormalization      79 84 88 90 103 140
Renormalization group equation      85Ч87 110Ч112
Representation of group centre      53Ч56
Representations of compact Lie algebras      Chapter 4
Representations of compact Lie groups      Chapter 5
Residual symmetry group      89
Rigid (symmetry) group      63 77Ч79
Root diagram      30Ч32
Rules for GUT models      118Ч120
S-matrix      101
Safe groups, representations      84
Semi-simple algebra, group      23Ч25 27 123
Simple connectivity      8 11
Simple group GUT-models      121
Simple group, algebra      23Ч25 27Ч35
SO(10) GUT model      117
SO(n) groups      10 11 34 43 45Ч46 53Ч54 57 117 121Ч124 130
Spinor representations      42 45Ч48 117 119
Spontaneous symmetry breaking      Chapters 8 10 12
Stability subgroups      89
Standard electro weak model      103Ч107
Strange quarks      70
Strata      128Ч132 135Ч136
String theory      123
Strong interactions      70
Structure constants      15 18 19 24 26 29Ч32 60
Structure functions      13Ч19
Structure theorem for compact Lie algebras      27
SU(2) orbits      129Ч130
SU(5) GUT model      113Ч117
SU(N)      23 34 43Ч44 53Ч56 59 84 86 119 121 123Ч124 131Ч134 137 142Ч149
Subalgebras      22 23
Subgroups      4
Sum (direct, semi-direct)      23
Superconductivity      96 126
Supersymmetry      123 126 152Ч153
Symmetric algebra      132Ч134
Symmetric tensor representation      130Ч131 134 136Ч137 142Ч144
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 15Ч21
Technicolour      124Ч125
Tensor representations      42Ч44 131Ч134
TeV experiments      127
Theta-vacua      126
Top quark      71 118
Topological charge      83 134
Topology of coset      128Ч129
Topology of group      7Ч9
Triality      53Ч54 69
True group      52Ч56
Unified gauge theory (UGT)      Chapters 7 9
Unitarity of representations      50
Unitary groups      11 23 34 53Ч56 77 Chapter
Unitary trick      35
Vectorlike assignment      84
W and Z mesons      71 88 103Ч104 107
Weak angle      104 106 112 118 122
Weak hypercharge      105
Weak interactions      68Ч69 101 103Ч107
Weight diagrams      36Ч38
Weyl character formula      38Ч39 58
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