Nash C. — Differential Topology and Quantum Field Theory :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Nash C. — Differential Topology and Quantum Field Theory

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

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

-vector bundle      125
-polynomial      112 340—341
Abelian differential      143
Abelian gauge theory      295 343—344 348
Abelian group      170 185
Abelian representation      325
Abelian semi-group      67 90
Abelian sub-group      188 (see also under Torus)
Adiabatic limit      284 288 290
Adjoint bundle      176
Affine space      216
Alexander polynomial      340—342
Algebraic curve      169
Algebraic varieties      137—139
Algebraic varieties, sub-manifold of      138
Amp $\grave{e}$ re’s law      344—345
Analytic torsion      348—349
Analytical index      93 97 120 126
Anharmonic ratio      314
anomalies      269—300
Anomalies, complex      290—291
Anomalies, for strings      281—283
Anomalies, global      283—290
Anomalies, gravitational      279—281
Anomalies, Hamiltonian approach to      292—300
Anomalies, local      269—283
Anomalous dimension      302
Arithmetic genus      107
Atiyah-singer index theorem      89 90—136
Axial current      272
Banach space      48 171
Base point      5—6
Base point, and       172
Base point, and gauge transformations      176 232
Base point, and homotopy      8 10 17—18 20
Base point, and K-theory      69—70 72
Beltrami differential      157 161
Beltrami equation      157
Bessel’s equation      35
Betti number      104 172 192 207
Betti number, and Hodge numbers      108
Betti number, and Laplacians      41 209
Betti number, and Morse theory      194 211
Betti number, and the instanton deformation complex      238
Betti number, and the Poincar $\acute{e}$ series      193
Betti number, of $S^{\infty}$       204
Betti number, of $\textbf{CP}^{n}$       197
Bianchi identity      228 243
Bifurcation      198
Bogomolny equation      243—246
Bogomolny equation, in hyperbolic space      247—251
Borel subgroup      189
Borel-Weil construction      188—191
Bott periodicity      11 75 78 95
boundary conditions      127
Boundary conditions, and Floer homology      328 337
Boundary conditions, and monopoles      244
Boundary conditions, non-local and the index theorem      128 131—133
Boundary conditions, periodic      311
Bundle automorphisms      175 (see also Gauge transformations)
Callan — Symanzik equations      301
Canonical bundle      139 (see also Determinant bundle)
Cartan matrix      24
Casimir operator      181—183
Casson invariant      330
Categories      see also Lusternik-Schnirelmann category
Categories and conformal field theory      321
Cauchy data      30
Cauchy problem      30
Cauchy — Riemann equations      64
Cauchy — Riemann operator      34 281
Cauchy’s Theorem      29
Cell decomposition      323
Cellular approximation theorem      323
Central charge      174
Central charge, and conformal field theory      307—308
Central extensions      179 (see also group extensions)
Central extensions, and the loop group      173 180 183 191
Central extensions, and the Virasoro group      174
Character ring      125
Characteristic class      16 78—79 82 85 108 112 133 239 278 280 290
Characteristic class, and invariant polynomials      87
Characteristic class, and obstruction theory      23
Characteristic class, and the index formula      98 101—103
Characteristic polynomial      135
Chern character      78—80 88 105 237 239 280 282
Chern character, and K-theory      81
Chern character, and the index formula      98
Chern class      16 79—82 105—106 134 142 180 189 219 222 237 245 248 277 286 297 334
Chern class, and line bundles      145—146
Chern class, and the Euler class      87
Chern class, and the Pontrjagin class      84—85
Chern — Simons      see also Knots
Chern — Simons, action      331 342—344 348 350 358 360
Chern — Simons, class      223 227
Chern — Simons, form      227
Chern — Simons, function      324—327 330
Chiral Fermion      270 271
Chow’s theorem      138
Classifying space      16 23
Classifying space and equivariant cohomology      202—204
Classifying space, and differentiable structures      19
Classifying space, and Fredholm operators      293
Classifying space, and vector bundles      70—71 74
Clifford algebra      114
Clover leaf knot      340—341
Cocycle      145 298
Cocycle, and group extensions      179 184—185
Cohomology      3 12—13 41 65 145 280 283 323 326 333-
Cohomology ring      15—16 95 120 220
Cohomology ring, and       79
Cohomology ring, and torsion      195
Cohomology, de Rham      see de Rham cohomology
Cohomology, Dolbeault      see Dolbeault cohomology
Cohomology, for sheaves      see sheaf cohomology
Cohomology, for vector bundles      see K-theory
Cohomology, local      279
Compact support      46
Compact support, and K-theory      90—91
Compact support, and test functions      50
Compactification      91 334 339
Compactification divisor      319
Complex manifolds      63 65 89 117 189 255 290—291
Complex manifolds, and algebraic geometry      138—139 142
Complex manifolds, and Morse theory      197
Complex manifolds, and the Dolbeault complex      106—108
Complex powers of elliptic operators      46
Complex structure      84 147 190 315 322
Complex structure of Riemann surfaces      139 149—155 241
Complex structure, and anomalies      291
Complex structure, and hyperk $\ddot{a}$ hler manifolds      255
Complex structure, and strings      260—262
Complex structure, and vector bundles      84
Complex vector bundle      see under vector bundle
Complexification      83—84 98 103 106 120 237
Complexification, of Lie groups      189—190
Complexification, of vector bundles      83—84
Comultiplication      8
Configuration space, and conformal field theory      320
Configuration space, for instantons      218—219 232 242 258
Configuration space, for monopoles      254
Configuration space, for strings      261
Conformal anomaly      180 262 281—283
Conformal block      315 317 319 321 321 350 356
Conformal family      309—317
Conformal field theory      306—321
Conformal field theory, and knot theory      343 350 354—355
Conformal Field Theory, rational      313
Conformal invariance      174 247 258 301 311 314 317
Conformal invariance, and conformal field theories      301 311 314 317

Conformal invariance, and strings      281—283
Conformal invariance, and the Virasoro group      174
Conformal invariance, and Yang — Mills theories      247 258
Conformal Killing vector      159 262
Conformal weight      312 355
Conjugate bundle      82
Connected sum      335 336 351
Connections      see also Instantons and monopoles
Connections, flat      323—326 330—331
Connections, Levi — Civita      270
Connections, projectively flat      320
Connections, reducible      232 240 323
Connections, Yang — Mills      118 270 279 281
Continuous section      219
Contractibility      96 156 204 245
Contractibility, and Fredholm operators      293
Contractibility, and universal bundles      96 218—219 245 258 327
Coupling constant      273 335 343 345—346
Covering space      139 153 156 255
Critical dimension      180 269 281
Critical points      192—201 204 206—207 209—213 301 323
Critical points, and flat connections      323—326 330—331
Critical points, and instantons      228—230
Critical points, and monopoles      242—243 255—259
Critical points, and phase transitions      301
Critical points, and the Hessian      193
Critical points, non-degenerate      193
Current algebra      173 177—178 185 299
De Rham cohomology      3 41 280 283 323 326 333
de Rham cohomology, and loop groups      179
de Rham cohomology, via sheaves      63 65
de Rham complex      13 93 108 116 124 238 323
de Rham complex, index of      103—104 106 116
Dedekind $\eta$ -function      312—313
Dehn twist      156 309 355
Descendant of a primary field      309
Determinant bundle      139
Determinant bundle, and index theory      276—278 283—286
Determinant line bundle      see determinant bundle
Diagonalisable matrices      88
Differentiable structure      2 23 26 338—339
Differentials of first kind      see Abelian differentials
Dilation      301—302 308
Dimensional reduction      250
Dirac operators      113—114
Dirac operators, and anomalies      269—281 283—296
Dirac operators, families of      275
Dirac operators, gauge covariance of      271
Dirac operators, index in twisted case      118
Dirac operators, index of      115—116
Direct limit      19 57
Discrete series      186
Distributions      49—51
Divisor      139—142 146
Divisor, and conformal field theory      319
Divisor, and Weierstrass gap theorem      166—167
Dolbeault cohomology      65 145
Dolbeault cohomology, and the Riemann moduli space      160
Dolbeault complex      106
Dolbeault complex index of      107 117
Donaldson’s polynomial invariants      334 336 338—339
Donaldson’s theorem      25—26 240—241
Doughnut      196—197 199
Dual bundle      107
Dyons      256
Effective action      288—289
Eilenberg and Steenrod      65
Eilenberg — MacLane space      12
Elliptic complex      91—96 103—104 124 126
Elliptic complex, and instanton moduli      235
Elliptic complex, and monopole moduli      251
Elliptic operators      27—55 162 327 348
Elliptic operators, and instanton deformations      237
Elliptic operators, and strings      261—268
Elliptic operators, as Fredholm operators      53—55
Elliptic operators, definition of differential      33 38
Elliptic operators, definition of pseudo-differential      42—43
Elliptic operators, families of      119
Elliptic operators, index theory of      89—136
Elliptic operators, of order $2\lambda +\epsilon$       45
Ellipticity      27—33 (see also hypo-ellipticity)
Energy functional      205 326
Energy functional, for geodesics      205
Energy functional, for monopoles      242 255—256
Energy momentum tensor      181 335
Energy momentum tensor, of conformal field theories      304 308 319—320
Equivariant cohomology      201—203
Equivariantly perfect function      204—205 258
Euler class      16 86—87 103—106 117 134 203
Euler — Poincar $\acute{e}$ characteristic      3
Evaluation map      221—224
Exceptional groups      170
Exceptional Lie algebra $E_{8}$       24
Exotic differentiable structure      23
Exotic differentiable structure, on $\textbf{R}^{4}$       26
Exotic sphere      23 192 285—286
Exterior algebra      94
Exterior algebra, and Fock space      297
Exterior algebra, and Hopf algebras      221—222
External product      76
Extremum      205 (see also Critical points)
Faddeev — Popov ghosts      218 347
Fake $\textbf{R}^{4}$       26
Families index theorem      119—122
Families index theorem for real families      121—122 284
Families index theorem, and anomalies      273—296
Family      see also families index theorem
Family, conformal      309—317
Family, of -bundles      220
Family, of conformal Killing vectors      165
Family, of connections      224 228 233 241 251—252
Family, of elliptic operators      119—122 269 275—297 326
Family, of Riemann surfaces      139
Family, of supersymmetric algebras      209
Fibration      17—19 120
Fibration, and differentiable structures      20—22
Fibration, and homotopy lifting property      17
Fibration, automorphism of      175
Fibration, of Hopf      78
Fibre bundle      14—19 287
Fibre bundle, and elliptic families      119
Fine sheaf      64 146
Fixed points      123—127 150 301
Fixed points, and index theory      123—137
Fixed points, of group actions      150 153—156 201 217—218 232
Flat connections      244 325 346—350
Floer homology      321—331
Floer homology, and Donaldson invariants      336—338
Fock space      297—299
Four manifolds      23—26 331—338
Fourier transform      28 31—34 37 44 48 52
Fractional integration      44
Framing of knots      345 354—355
Fredholm operators      54—55 292—294
Fredholm operators, and K-theory      88 292
Fredholm operators, from elliptic operators      53—55
Fredholm operators, self-adjoint      293—294
Fredholm operators, skew-adjoint      294
Free action      150 232
Fubini — Study metric      147
Fuchsian group      161
Functional integral      218 321
Functional integral, and anomalies      271—275 288
Functional integral, and Donaldson invariants      336
Functional integral, and knots      344—348 351
Functional integral, for strings      260
functors      7 293—294
Fundamental group      5—6 9—10 153—154 340
Fundamental solution      28
Fusion rules      313 316—317 321

1 2 3

О проекте