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Nash C. Ч Differential Topology and Quantum Field Theory
Nash C. Ч Differential Topology and Quantum Field Theory

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Ќазвание: Differential Topology and Quantum Field Theory

јвтор: Nash C.

јннотаци€:

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: en

–убрика: ћатематика/ћатематическа€ ‘изика/

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

ed2k: ed2k stats

√од издани€: 1991

 оличество страниц: 386

ƒобавлена в каталог: 24.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$G$-vector bundle      125
$L$-polynomial      112 340Ч341
Abelian differential      143
Abelian gauge theory      295 343Ч344 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      340Ч342
Algebraic curve      169
Algebraic varieties      137Ч139
Algebraic varieties, sub-manifold of      138
Amp$\grave{e}$reТs law      344Ч345
Analytic torsion      348Ч349
Analytical index      93 97 120 126
Anharmonic ratio      314
anomalies      269Ч300
Anomalies, complex      290Ч291
Anomalies, for strings      281Ч283
Anomalies, global      283Ч290
Anomalies, gravitational      279Ч281
Anomalies, Hamiltonian approach to      292Ч300
Anomalies, local      269Ч283
Anomalous dimension      302
Arithmetic genus      107
Atiyah-singer index theorem      89 90Ч136
Axial current      272
Banach space      48 171
Base point      5Ч6
Base point, and $Map(X,G)$      172
Base point, and gauge transformations      176 232
Base point, and homotopy      8 10 17Ч18 20
Base point, and K-theory      69Ч70 72
Beltrami differential      157 161
Beltrami equation      157
BesselТs 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      243Ч246
Bogomolny equation, in hyperbolic space      247Ч251
Borel subgroup      189
Borel-Weil construction      188Ч191
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 131Ч133
Boundary conditions, periodic      311
Bundle automorphisms      175 (see also Gauge transformations)
Callan Ч Symanzik equations      301
Canonical bundle      139 (see also Determinant bundle)
Cartan matrix      24
Casimir operator      181Ч183
Casson invariant      330
Categories      see also Lusternik-Schnirelmann category
Categories and conformal field theory      321
Cauchy data      30
Cauchy problem      30
Cauchy Ч Riemann equations      64
Cauchy Ч Riemann operator      34 281
CauchyТs Theorem      29
Cell decomposition      323
Cellular approximation theorem      323
Central charge      174
Central charge, and conformal field theory      307Ч308
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 78Ч79 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 101Ч103
Characteristic polynomial      135
Chern character      78Ч80 88 105 237 239 280 282
Chern character, and K-theory      81
Chern character, and the index formula      98
Chern class      16 79Ч82 105Ч106 134 142 180 189 219 222 237 245 248 277 286 297 334
Chern class, and line bundles      145Ч146
Chern class, and the Euler class      87
Chern class, and the Pontrjagin class      84Ч85
Chern Ч Simons      see also Knots
Chern Ч Simons, action      331 342Ч344 348 350 358 360
Chern Ч Simons, class      223 227
Chern Ч Simons, form      227
Chern Ч Simons, function      324Ч327 330
Chiral Fermion      270 271
ChowТs theorem      138
Classifying space      16 23
Classifying space and equivariant cohomology      202Ч204
Classifying space, and differentiable structures      19
Classifying space, and Fredholm operators      293
Classifying space, and vector bundles      70Ч71 74
Clifford algebra      114
Clover leaf knot      340Ч341
Cocycle      145 298
Cocycle, and group extensions      179 184Ч185
Cohomology      3 12Ч13 41 65 145 280 283 323 326 333-
Cohomology ring      15Ч16 95 120 220
Cohomology ring, and $K(X)$      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      90Ч91
Compact support, and test functions      50
Compactification      91 334 339
Compactification divisor      319
Complex manifolds      63 65 89 117 189 255 290Ч291
Complex manifolds, and algebraic geometry      138Ч139 142
Complex manifolds, and Morse theory      197
Complex manifolds, and the Dolbeault complex      106Ч108
Complex powers of elliptic operators      46
Complex structure      84 147 190 315 322
Complex structure of Riemann surfaces      139 149Ч155 241
Complex structure, and anomalies      291
Complex structure, and hyperk$\ddot{a}$hler manifolds      255
Complex structure, and strings      260Ч262
Complex structure, and vector bundles      84
Complex vector bundle      see under vector bundle
Complexification      83Ч84 98 103 106 120 237
Complexification, of Lie groups      189Ч190
Complexification, of vector bundles      83Ч84
Comultiplication      8
Configuration space, and conformal field theory      320
Configuration space, for instantons      218Ч219 232 242 258
Configuration space, for monopoles      254
Configuration space, for strings      261
Conformal anomaly      180 262 281Ч283
Conformal block      315 317 319 321 321 350 356
Conformal family      309Ч317
Conformal field theory      306Ч321
Conformal field theory, and knot theory      343 350 354Ч355
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      281Ч283
Conformal invariance, and the Virasoro group      174
Conformal invariance, and Yang Ч 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      323Ч326 330Ч331
Connections, Levi Ч Civita      270
Connections, projectively flat      320
Connections, reducible      232 240 323
Connections, Yang Ч Mills      118 270 279 281
Continuous section      219
Contractibility      96 156 204 245
Contractibility, and Fredholm operators      293
Contractibility, and universal bundles      96 218Ч219 245 258 327
Coupling constant      273 335 343 345Ч346
Covering space      139 153 156 255
Critical dimension      180 269 281
Critical points      192Ч201 204 206Ч207 209Ч213 301 323
Critical points, and flat connections      323Ч326 330Ч331
Critical points, and instantons      228Ч230
Critical points, and monopoles      242Ч243 255Ч259
Critical points, and phase transitions      301
Critical points, and the Hessian      193
Critical points, non-degenerate      193
Current algebra      173 177Ч178 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      103Ч104 106 116
Dedekind $\eta$-function      312Ч313
Dehn twist      156 309 355
Descendant of a primary field      309
Determinant bundle      139
Determinant bundle, and index theory      276Ч278 283Ч286
Determinant line bundle      see determinant bundle
Diagonalisable matrices      88
Differentiable structure      2 23 26 338Ч339
Differentials of first kind      see Abelian differentials
Dilation      301Ч302 308
Dimensional reduction      250
Dirac operators      113Ч114
Dirac operators, and anomalies      269Ч281 283Ч296
Dirac operators, families of      275
Dirac operators, gauge covariance of      271
Dirac operators, index in twisted case      118
Dirac operators, index of      115Ч116
Direct limit      19 57
Discrete series      186
Distributions      49Ч51
Divisor      139Ч142 146
Divisor, and conformal field theory      319
Divisor, and Weierstrass gap theorem      166Ч167
Dolbeault cohomology      65 145
Dolbeault cohomology, and the Riemann moduli space      160
Dolbeault complex      106
Dolbeault complex index of      107 117
DonaldsonТs polynomial invariants      334 336 338Ч339
DonaldsonТs theorem      25Ч26 240Ч241
Doughnut      196Ч197 199
Dual bundle      107
Dyons      256
Effective action      288Ч289
Eilenberg and Steenrod      65
Eilenberg Ч MacLane space      12
Elliptic complex      91Ч96 103Ч104 124 126
Elliptic complex, and instanton moduli      235
Elliptic complex, and monopole moduli      251
Elliptic operators      27Ч55 162 327 348
Elliptic operators, and instanton deformations      237
Elliptic operators, and strings      261Ч268
Elliptic operators, as Fredholm operators      53Ч55
Elliptic operators, definition of differential      33 38
Elliptic operators, definition of pseudo-differential      42Ч43
Elliptic operators, families of      119
Elliptic operators, index theory of      89Ч136
Elliptic operators, of order $2\lambda +\epsilon$      45
Ellipticity      27Ч33 (see also hypo-ellipticity)
Energy functional      205 326
Energy functional, for geodesics      205
Energy functional, for monopoles      242 255Ч256
Energy momentum tensor      181 335
Energy momentum tensor, of conformal field theories      304 308 319Ч320
Equivariant cohomology      201Ч203
Equivariantly perfect function      204Ч205 258
Euler class      16 86Ч87 103Ч106 117 134 203
Euler Ч Poincar$\acute{e}$ characteristic      3
Evaluation map      221Ч224
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 285Ч286
Exterior algebra      94
Exterior algebra, and Fock space      297
Exterior algebra, and Hopf algebras      221Ч222
External product      76
Extremum      205 (see also Critical points)
Faddeev Ч Popov ghosts      218 347
Fake $\textbf{R}^{4}$      26
Families index theorem      119Ч122
Families index theorem for real families      121Ч122 284
Families index theorem, and anomalies      273Ч296
Family      see also families index theorem
Family, conformal      309Ч317
Family, of $G$-bundles      220
Family, of conformal Killing vectors      165
Family, of connections      224 228 233 241 251Ч252
Family, of elliptic operators      119Ч122 269 275Ч297 326
Family, of Riemann surfaces      139
Family, of supersymmetric algebras      209
Fibration      17Ч19 120
Fibration, and differentiable structures      20Ч22
Fibration, and homotopy lifting property      17
Fibration, automorphism of      175
Fibration, of Hopf      78
Fibre bundle      14Ч19 287
Fibre bundle, and elliptic families      119
Fine sheaf      64 146
Fixed points      123Ч127 150 301
Fixed points, and index theory      123Ч137
Fixed points, of group actions      150 153Ч156 201 217Ч218 232
Flat connections      244 325 346Ч350
Floer homology      321Ч331
Floer homology, and Donaldson invariants      336Ч338
Fock space      297Ч299
Four manifolds      23Ч26 331Ч338
Fourier transform      28 31Ч34 37 44 48 52
Fractional integration      44
Framing of knots      345 354Ч355
Fredholm operators      54Ч55 292Ч294
Fredholm operators, and K-theory      88 292
Fredholm operators, from elliptic operators      53Ч55
Fredholm operators, self-adjoint      293Ч294
Fredholm operators, skew-adjoint      294
Free action      150 232
Fubini Ч Study metric      147
Fuchsian group      161
Functional integral      218 321
Functional integral, and anomalies      271Ч275 288
Functional integral, and Donaldson invariants      336
Functional integral, and knots      344Ч348 351
Functional integral, for strings      260
functors      7 293Ч294
Fundamental group      5Ч6 9Ч10 153Ч154 340
Fundamental solution      28
Fusion rules      313 316Ч317 321
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