Lopuzanski J. — An introduction to symmetry and supersymmetry in quantum field theory :: Электронная библиотека попечительского совета мехмата МГУ

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Lopuzanski J. — An introduction to symmetry and supersymmetry in quantum field theory

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Название: An introduction to symmetry and supersymmetry in quantum field theory

Автор: Lopuzanski J.

Аннотация:

This is a set of lecture notes given by the author at the Universities of Gцttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.

Язык:

Рубрика: Физика/Квантовая теория поля/Суперсимметрия, супергравитация/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 373

Добавлена в каталог: 18.09.2005

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Предметный указатель

$E_{2}$       322
$L^{\uparrow}_{+}$       56
$P^{\uparrow}_{+}$ dagger      72 73
$sl(2,\mathbb{C})$       46 48 50 52—56 60 64 66 84 87 267 268 315
$SL(2,\mathbb{C})$ transformations      55 56 58 60 61
$Sp(2,\mathbb{C})$       267
$Sp(2,\mathbb{C})=SL(2,\mathbb{C})$       267
$Sp(k,\mathbb{C})$       267 268
$Sp(n,\mathbb{C})$       275
$S_{\mu\nu}$       81
$U(a,\Lambda)$       72
$W^{2}$       314
$\mathcal{D}^{(0,1)}$       63
$\mathcal{D}^{(1,0)}$       60
$\mathcal{D}^{(1/2,1/2)}$       60
$\mathcal{D}_{\Omega}$       79 81 133 135 155
$\varepsilon_{\mu\nu\chi\lambda}$       62
Abelian gauge transformations      165
Abelian group      222
Abnormal commutation relations      84
Adjoint operator      35
Adler — Bell — Jackiw Anomaly      180
Algebra of an abelian group      222
Almost and weak locality      122 176
Almost and weakly local field      196
Almost locality      117 118
Analytic vector      191
Annihilation operator      26 321
anomalies      129 179 180 182 187
Anomalous dimension      170
Antilinear operations      113
Antilinearity      114
Antilocal field      82 84 85
Antiparticle      321
Antiself-duality      62
Antisymmetric tensor      62
Antisymmetric tensor, antiself-dual      61 63
Antisymmetric tensor, symplectic      46
Antiunitarity      114
Antiunitary operator      110 113
Approximate symmetry      2 3 7
Asymptotic free fields      190 225
Axiom 0      104 105
Axiom 1      28 31 71 73 91 160 171
Axiom 2      38 40
Axiom 3      66 73 115 133 154 313
Axiom 4      32 69 71 75 77 78 91 92 115 140 189 236 253 340 342
Axiom 5      81—83 91 92 341
Axiom 6      69 91 101—103 334
Axiomatic field theory      3 4 7 33
Axiomatic quantum field theory      3 8 10 128 244
Baby model      258
Banach space      30
Baryon number      163
Bianchi identity      181
Bispinor(s)      309
Bo sonic current      222
Borchers’ classes      6 115 117 121 123
Bose — Einstein statistics      83
Bosonic charge      221 222 224 279 281
Bounded functional      31
Bounded linear operator      34
Bounded operator      34 36
Bounded self-adjoint operator      37
Boundedness      34
Broken symmetries      279
C* algebra      12
Canonical anticommutation relations      44 85 302 327
Canonical commutation relations      5 27 166 253
Canonical dimension      170
Canonical formalism      9 10
Canonical variables      20
Carruthers’ Theorem      176 178 179
Casimir operator      6 54 69 75 313 314
Cauchy sequence      29
Cauchy series      33
Causality      81 83
Center of algebra      222
Center of superalgebra      239
Central charge(s)      229 231 236 238—241 249 250 252 264 265
Charge conjugation      8 113
Charged sectors      166
Charged state      163 167
Charges      126 127 169 171 235 300
Chiral covariance      180
Clifford algebra      47 48 253
Closable operator      36
Closed extension      36
Closed operator      35 36
Closure      33 34
Cluster Decomposition Theorem      151 153
Coherent space      106
Coherent subspace(s)      105 110
Coleman — Mandula Theorem      200 201 221 223 226 227 230—232 278
Coleman — Mandula, No-Go Theorems      7 189 194 197 198 202 205 218
Commutation relations      9—11 19 20 23 24 44
Compact group      66 222 242
Compact Lie group algebra      222
Complete normed linear space      28 33 40
Complete space      34
Completeness      30
Completion      33
Complex field      106
Conformal current      169
Conformal mapping      7
Conformal symmetry      169 284 290
Conformally covariant theory      170
Conserved currents      161 162
Conserved quantity      124—128 189 190 201
Constant of motion      125 183 189 201
Continuity      34
Continuity equation      126
Continuous functional      31
Continuous linear functional      31 40
Continuous operator      34
Contravariant components      309
Contravariant spinor components      54 55
Covariant components      56
Creation operator      26 321
Current conservation      139 146
Current conservation, anomalous behaviour      180
Current(s)      126 128 133 135 157 193
Cyclic vacuum state      89
Cyclic vector      90
Degree of a bosonic charge      235
Degree of a charge      231 279
Delta of Jordan and Pauli      24 94
Dense domain of definition      39
Dense set      33—36
Dilatation current      169
Dilatation symmetry      5 290
Dilatation symmetry, spontaneous breaking      171
Dilatational covariance      170
Dilatational group      284
Dilatational mappings      7
Dilatational transformation      284
Dilatationally covariant theory      170
Dilatations      127 169
Dimension of the field      290
Dimensional parameter      289
Dimensional reflection      290 298 300
Dirac equation      309 312
Dirac — Fermi statistics      83
Discontinuous operator      35
Discrete symmetry      8 114
Dispersion relations      11
Distributions      17 19—21 25 42—44
Domain of operator definition      34
Dotted components      55
Dotted indices      53 55

Dotted spinor      309
Dotted spinor tensor      60
Dual tensor      61
Dynamical symmetries      7
Einstein’s causality principle      82
Electrodynamics      165
Energy      127
Energy momentum tensor      127 169 171 187 290
Equations of motion      9 351 353
Equivalence class      41 42
Essentially self-adjoint charge      154
Essentially self-adjoint operator      37 44
Euclidean rotations      322
Euclidean space      15
Euclidean translations      322
Euler equations of motion      10
Event      28
Exact symmetry      2 3
Extended supersymmetry      259
Extension      37
Factor group      238 300
Faithful representation      66
Fermi — Dirac statistics      83 85
Fermionic charges      179 224 225 235 244 291 300
Field      38 39
Field algebra of bounded operators      170
Field equations      10
Field functional      39
Field operator      45
Finite dimensional representation      66
Fock construction      32
Fock representation      22
Fock space      23 166 191 252 253
Fock vacuum      22 26 100 191 253 260—262
Free field theory      24 44
Free field(s)      11 15 18—20 43 124
Free massive field      320
Free neutral spinor field      85
Free quantum fields      313
Free real scalar field      44
Free smeared scalar field      44
Fundamental (Cauchy) sequence      29
Fundamental bosonic charges      222 226
Fundamental charges      226
Fundamental fermionic charges      226
Fundamental sequences      41
Galilean symmetry      2
Gamma matrices      309 311 312
Gauge      127
Gauge charges      129 161 165
Gauge covariance      167
Gauge current      127
Gauge field theory/theories      4 126 161 167
Gauge Fields      2 33 182
Gauge invariant observables      167
Gauge theories      180
Gauge transformations, first kind      127
Gauge transformations, second kind      167
Gauss’ law      161—163 166 167
Gauss’ Theorem      118 160
Generators      49 51—54 65 67 126 128 135 295
Generators of $SL(2,\mathbb{C})$       50 78
Generators of $\mathfrak{B}_{0}$       66
Generators of a symmetry      189 190
Generators of SU(N)      296
Generators of supersymmetry      223
Generators of the Lorentz group      75
Generators of the Poincare group      199
Generators of the U(a,A) group      66
Generators of translations      76 78 81
Geometrical charge      221
Geometrical field transformations      45
Geometrical symmetries      7 221
Global conserved quantities      127
Global gauge transformations      162
Global supersymmetry      8
Global symmetry      7 115 122 124 125 196
Goldstone particles      157 158 171
Goldstone’s theorem      141 157 158
Ground state      19 20
Group(s)      6 8 13 25
Group(s) of conformal transformations      284
Group(s) of translations      45
Haag — Ruelle scattering theory      191
Hahn — Banach theorem      31
Half-integral spin field      85
Heisenberg picture      19 102
Helicity      70 79 322 324
Helicity operator      322 324
Hermitian adjoint operators      20
Hermitian current      193
Hermitian generator      52
Hermitian matrix      48
Hermitian operator      35 36
Hermitian spinor tensor      58 59
Hilbert space      19 21 23 24 28 30 31 33 36 37 39 66 165
Homomorphism      298
Ideal      237 238 300
Incoming and outgoing fields      334
Incoming free asymptotic fields      92
Inelastic scattering      104
Inequivalent representations      53
Infinite-dimensional representations, $\mathfrak{B}_{0}$ group      66 75
Infrared divergences      279
Infrared states      167
Interacting fields      44 195
Interacting interpolating field      196
Interacting real scalar field      44
Internal symmetry      7 125 126 222 230 237 285
Internal symmetry group      197 242 300
Interpolating fields      195
Intertwiner      236 240 241 264 265 266 268 269 273
Invariant internal group      199
Inverse Noether’s Theorem      135 161
Inverse of Poincare lemma      181
Irreducible algebra of observables      106
Irreducible field algebra      89—91
Irreducible multiplet      252 254
Irreducible representation      66
Irreducible representation, $SL(2,\mathbb{C})$       54 57 63
Irreducible representation, $\mathcal{D}^{(1,0)}$       60 63
Irreducible representation, $\mathcal{D}^{(3/2,0)}$       61
Irreducible representation, $\mathfrak{B}_{0}$       69 70 75 79
Irreducible set of fields      118
Irreducible vector      90
Jacobi identity      49 144 256
Jordan — Pauli delta      44
Jost points      113
Jost — Lehmann — Dyson representation      154
Jost — Schroer Theorem      95 339 342 343
Kallen — Lehmann spectral decomposition      44
Kernel      238 298—300
Klein transformation      84
Klein — Gordon equation      15 16 18 19 20 94 96 118 120 206 207 258 312 314 320 332 333 342
Lagrange formalism      9
Lagrange function      128
Lagrangian      9—11 15 16 351
Lie algebra      49 52 237 265 268
Lie algebra, SU(2)      240
Lie algebra, uSp(N)      268
Lie group      8 49 67
Lie — Cartan relations      49 51 52 56 65 81 221 223
Light cone      26
Linear continuous functional      345
Linear functional(s)      30 31 34
Linear operator      34 35
Linear space      28 33 38
Little group of $L^{\uparrow}_{+}$       315 322
Local conserved quantities      127
Local current      171 193

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