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Nash C. — Differential Topology and Quantum Field Theory

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Название: Differential Topology and Quantum Field Theory

Автор: Nash C.

Аннотация:

The remarkable developments in diferential topology and how these recent advances have been applied as a primary research tool on quantum field theory are presented in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following on from his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers ellipitc differential and pseudo-differential operators, Atiyah-singer Index theory, Morse theory, instanntons and monopoles, topological quantum field theory, string theory and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time.

Язык:

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 386

Добавлена в каталог: 24.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Saddle point      196—198
Scalar curvature      236 238—239 249
Scale dimension      302
Scale invariance      303—304
Schr $\ddot{o}$ dinger equation      31 34 210
Schwarzian derivative      307
Schwinger term      178 299
Second fundamental form      135—136
Secondary characteristic classes      223—227 324
Self-dual curvature      25 229—236 245—247
Self-dual manifold      236
Self-duality equations      see under instantons
Semi-direct product      183 261 281
Semi-group      67 88—90
Serre duality      144—145 161—164 169 319
Sheaf cohomology      56—57 59—65 144—145 164 167 189
Sheaf morphism      60
Sheaves      56—59
Sigma model      181 258
Signature complex      108—110 118
Signature operator      118 128 131—133
Simply connected      23—25 113 150—151 173 240 244 275 327 333
Singular support      30 47
Skein relation      342 351 353—355
Skein relation, for the Alexander polynomial      342
Skein relation, for the Jones polynomial      342 351 353—355
Smash product      6
Smooth manifold      23 26 152
Smooth section      37 59
Smooth structure      23 26
Smoothability      24 242 332
Smoothing operator      46 54—55
Sobolev space      47—55
Sobolev space, and Sobolev embedding theorem      52
Soft sheaf      63
Spectral flow      284 295—296 326—327 330-331
Spectral sequence      17 19
Spin complex      113—114 118 277 282
Spin structure      113
Spin-manifold      113 270
Split exact sequence      70 179
Splitting principle      79—80 82 86—88 105 111 282
Stability group      150 232—233
Stable equivalence class      69 72
Stable range      72—74
Stable range, complex and quaternionic      74
Stable range, real      72
Stalk      57—58 60
Stationary phase      346
Stationary point      346
Steepest descent      212—214 326—327
Stiefel — Whitney classes      16 270
Stratification      196
String tension      259
String theory      259—268 289 316 318
String theory, critical dimension of      281—283
Sugawara construction      181 187
Supersymmetric field theory      335
Supersymmetric quantum mechanics      207—215
Supersymmetric string theory      286 289
Suspension      7 9 76
Symbol complex      91—94 102—104 106—107 110—111 114 121 126

Symbol space      43—44
Symplectic group      74 78
Symplectic manifold      147
Symplectic structure      350
System of functions      100—101
Tame knots      340
Teichmuller space      148—156 265
Test functions      51
Thom homomorphism      94—96
Todd class      78—79 82 98 100 105 112
Topological charge      244 337
Topological field theory      322—360
Topological index      89 94 96—97 120 122 126
Topological manifold      2 20—22 25
Topological quantum field theory      322—360
Topological quantum field theory, and knots, torsion      283 (see also Global anomaly)
Torus      147 151 311 356—358
Torus, maximal      188
Torus, Morse theory on      196 199
Torus, Teichm $\ddot{u}$ ller space for      153—156
Trace class      271
Transgression      224 298
Transition function      2 19 82—83 86 145
Trefoil      340 (see also clover leaf)
Triangle anomaly      269
Tubular neighbourhood      94—96 356
tunnelling      212—213 322 330
Unimodular      23 25
Universal coefficient theorem      284
Vanishing theorem      163—165 189
Vanishing theorem, for instantons      236
Vanishing theorem, of Kodaira      163 189
Variety      see algebraic varieties
Vector bundles, and ellipticity      36—41
Vector bundles, and K-theory      65—75
Vector bundles, and stable equivalence      65—68
Vector bundles, complex      65 74 81—87 103 107 121
Vector bundles, quaternionic      73—74
Vector bundles, real      70—74 83—86
Vertex operator      316
Virasoro algebra      174—175 180—183
Virasoro algebra, and conformal field theory      307—311 317
Virasoro algebra, representations of      185—187
Virtual dimension      68—69 282
Von Neumann algebras      341
Wave equation      29—30
Weierstrass gap theorem      167—168 319
Weierstrass points      166—169
Weil — Petersson metric      265—266
Weitzenb $\ddot{o}$ ck positivity      163 236
Weyl chamber      190 291
Weyl tensor      236
Whitney sum      79 82 84 86
Wilson line      343—344 356—357 360
Winding number      245 249
World sheet      259
Yang — Mills connection      118 270 279 281
Yang — Mills equations      25 229 230 242
Yang — Mills — Higgs system      246 250 256
Zero locus      137—138
zero modes      336
Zero section      38 43 92 94
Zeta function      131—132 261 273—274 283 348

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