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

Local current conservation      136 137 139
Local field      85 118 196 327
Local gauge covariance      180
Local gauge transformations      167
Local generator(s)      128 129
Local observables      12 166
Local operator      129
Local states      129 130 133 160
Local symmetry      7
Locality      33 84 163
Localizable charge      163
Localized operator      129 130 135 160
Localized states      130
Locally conserved current      126—129 135 137 139 142 157 167 171 189 193 222
Lorentz covariance      33 163
Lorentz group      6 18 46 56 60 163 170
Lorentz group, covering group      6
Lorentz invariance      25 26
Lorentz invariance, breakdown      166
Lorentz pseudorotations      127
Lorentz transformation(s)      2 5 6 18 25 46 47 59 60
LSZ approach      93
LSZ formalism      12 95—97 117
Majorana bispinor      310 311
Majorana representation      310—312
Mass gap      136 137 139 141 142 145
Mass operator      313
Mass squared operator      76
Massive fields      189
Massive gauge field theories      165
Massive one-particle states      91
Massive particles      93 166
Massive scalar interacting field      91
Massless free field      5
Massless Goldstone one-particle state      158
Massless particles      91 93 141 157 165 166 170 171 278
Massless Poincare group representation      172
Measureable quantities      28 37
Method of Haag, Ruelle, Hepp and Araki      97
Minkowski space      6 11 15 28 38 47 56 59 61 156 163
Mixed spinor tensor      59
Momentum tensor      168
Multidimensional Dirac delta      43
Multiplicative charges      165
Multiplicatively positive functional      345
Multiplicators      27
Nelson Theorem      191
Neutrality of free fields      327
Noether current      168 351 352
Noetherian charge      135 171
Noether’s theorem      126 127 351
Non-abelian fields      2
Non-abelian gauge charges      165
Non-Abelian gauge field theory      13
Non-compact connected group      66
Non-compact Lie group      64
Non-fundamental multiplets      258
Non-overlapping states      99 100 334 335 337 338
Norm      28 30 31 40
Norm of an operator      34
Normal commutation relations      84
Normed algebra, associative      345
Normed algebra, involutive      345
Normed linear space      29 31
Normed space      30
Number of spinor charges      246 249 251
O(N)      274
Observable(s)      105 106 110 165 167
One-particle state      26 77 100 101
Operator      19 28 36
Operator, closed extension of      36
Operator, self-adjoint      67
Operator-valued distribution(s)      19 20 38
Operators in the Hilbert space      33
Outgoing free asymptotic fields      92 93
O’Raifeartaigh’s Theorem      197 200 202 215 233 287
Pair-conjugate multiplets      178 179
Parastatistics      83 88
Particle interpretation      32
Particle number operator      26
Pauli exclusion principle      85 248
Pauli matrices      47 48 51 58
Pauli — Lubanski vector      70 78 79 246 313
PCT operator      114 121
PCT symmetry      113
PCT transformation(s)      113 114
Physical symmetries      108
Physically realizable rays      110
Physically realizable state      33 105
Poincare covariance      110 114 167
Poincare covariant current      171
Poincare group      6 8 18 101 124 129 197 284
Poincare invariant      189
Poincare representation      118
Poincare symmetry      122 124
Poincare transformation(s)      24 25 70 71 91 111 112
Poisson brackets      9
Polarization coefficients      317 321 327
Positive-definite metric      33
Principle of locality      166
Principle of relativity      2 5 6 82
Projective representations      71
Proper Lorentz group      56 65
Proper Lorentz transformation      56 60
Proper Poincare group      45 115
Proper Poincare transformation      72
Proper spinorial group      64 69
Pseudorotations      6
PTC mapping      8
PTC theorem      11
Quantum electrodynamics      166 167
Quantum field      5
Quantum field theory      1 3 5 8 12 28 35 75 109 244
Quantum modes, hidden      83
Quantum scalar free field      18
Quantum state      28
Quasilocal operators      140
Quasilocal state      129—131 133 142
Quaternion group      48
RANGE      39
Range of linear operator      34
Ray(s)      28 32 33 71
Real free scalar field      44
Reconstruction theorem      109 110 344
Reeh — Schlieder theorem      130 135 159 206 314 339 341 343 350
Reflection      8
Regular sequence(s)      41 42
Relatively local currents      193
Relativistic field thoery      5
Relativistic geometrical symmetries      115
Representation      66
Representation of $SL(2,\mathbb{C})$       54 57
Representation of $\mathcal{L}_{B}$       240
Representation of algebra      49
Representation of internal symmetry group      241
Representation of super-Lie algebra      246 252 301
Representation, $\mathcal{D}^{(0,0)}$       60
Representation, $\mathcal{D}^{(1/2,0)}$       61
Riemann — Lebsegue Lemma      184
Riesz theorem      31 35 132
S-matrix      103 116 117 121 123—126 170
Scalar charge      171 221
Scalar free field      15 32
Scalar massive field      15
Scalar product      28 30 31
Scattering Assumption      197 198 209 212
Scattering experiment      92
Scattering matrix      6 12

Scattering operator      6 103
Scattering probability amplitude      103
Scattering process      91 93
Scattering states      101
Scattering theory of Haag, Ruelle, Hepp and Araki      329
Schur’s lemma      54 90 265
Schwartz inequality      133
Schwartz nuclear theorem      109 340
Self-adjoint extension      37
Self-adjoint operator(s)      19 28 35—37 67 69 81 191
Self-adjointness of charges      154
Self-adjointness of generators      154
Self-conjugate multiplets      178 179
Self-dual field      74
Self-dual tensor      61 62
Semi-simple algebra      265
Semi-simple compact group      265
Semi-simple Lie algebra      222
Separability of $S_{n}$       40
Separability of the Hilbert space      40
Separable Hilbert space      28 31 32
Sesquilinear form      132 138 139
Set      33
Simply connected group      56
Skew symmetric tensor charge      221
Smeared out fields      45
SO(3)      318
SO(N)      274
Space of $S_{n}$       40
Space of convolutors      43
Space of multiplicators in $S_{n}$       43
Space of test functions      38
Space reflections      312
Space reflections, symmetry      309
Space translations      156
Space-time translations      127 166
Spacelike cones      165 186
Special conformal currents      169
Special conformal groups      169
Special conformal symmetry generators      285
Special conformal transformations      127 170 284
Special relativity      2
Spectral condition      75 110
Spectral decomposition      37
Spectral measure      76
Spectral projection operators      67
Spectral representation      67
speed of light      2
Spin and Statistics Theorem      11 84 85 136
Spin operator      313 315
Spinor      46 47 54
Spinor field      84
Spinor formalism      309
Spinor space      46 47 55 57
Spinor tensor      60
Spinorial charge(s)      226 229 230 231 236 238
Spinorial group      45 313 318
Spinorial tensor(s)      54 57
Spontaneously broken symmetry      7 141 157 158 160 161 179
Stability of the vacuum      101
Stablity of one-particle states      100
Stone’s theorem      66—68 75 128 154
Strangeness      163
Strictly interacting field theory      201
Strictly local states      129 130 138
Strictly localized operator      184
strings      165 186
Strong convergence      29 30 35 66
Structure constants      49 51 56 240
SU(2)      8 47 50 51 52 54 241 262 264 268 315 316 318
SU(3)      8
SU(4)      300
SU(N)      21 A 295 297 298 300
Super-Jacobi identity/identities      145 224 234 237 238 256 263 295 296 298
Super-Lie algebra      225 226 231 241 242 251
Superselection rule(s)      84 104 165 166 245 264
Superselection sector(s)      165 166
Superstring      186
Supersymmetric multiplet      225
Supersymmetry      1 4 7 8 179 230 244 259
Supersymmetry algebra      7 238
Supersymmetry generators      226
Swieca’s theorem      164 169
Symmetric (metric) tensor      46
Symmetric operator(s)      35—37
Symmetry      1—7 12 13 110 125 157 278
Symmetry algebra      7
Symmetry group      113 128
Symmetry of the Lagrangian      351
Symplectic Lie algebra      267
Symplectic space      46 47
Symplectic tensor      46 54 56
Tempered distribution(s)      38 40 44
Test function      42
Test function space      40
Thirring model      11 14
Time reflection      113
Time-ordered polynomial      118
Topological charges      126 129
topology      30
Translational generators      65
Translational group      6 25 64 65
Translationally non-covariant currents      167
Translations      6
Truncated      117
TVEV (truncated vacuum expectation value) functions      331—333 335
Twistors      87
U( 1)      305
U(4)      300
U(a,A)      66 73
U(n)      274 295—298 300
Unbounded operator      28 34 36 37 39
Unbounded self-adjoint operator      37
Undotted 2-dimensional representation      53
Undotted and dotted spinor(s)      55 57 309
Uniqueness of the vacuum      76 79 91
Unitarity of U(a, A)      66
Unitary implementation of conformal symmetry      288
Unitary operator      110
Unitary representations      22 66 103 165
Unitary transformation      22
Universal covering group      45
Universal covering group of Lorentz group      25 56
Universal covering group of Poincare group      65
USp(N)      274
VACUUM      79 81
Vacuum fluctuations      136
Vacuum state      77 89 100
Vector charge      221
Weak (anti)locality      113
Weak convergence      30 66
Weak locality      117 121 176
Weakly continuous representation      66
Weakly local field      117 196
Weinberg — Witten Theorem      169 171 174
Wess and Zumino, Baby model      258
Weyl equation      158
Wichmann Theorem      212
Wightman formalism      12 109 344
Wightman functional      108 110
Wightman functions      44 109 110 112 115 131 161 345 350
Wightman functions, cluster decomposition      110 131
Wightman theory      163
Wigner boosting procedure      316 321
Wigner phase      172 323
Yang — Feldman Equation (7)      93 97 100 102 114
Yang — Mills gauge fields      167
Yang — Mills gauge theory      33 185

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