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Cartier P., Julia B., Moussa P. — Frontiers in Number Theory, Physics, and Geometry II
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Название: Frontiers in Number Theory, Physics, and Geometry IIАвторы: Cartier P., Julia B., Moussa P.Аннотация: The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has recently become more prominent.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2007Количество страниц: 789Добавлена в каталог: 07.05.2008Операции: Положить на полку |
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148 134 153 155 150 153 135 150 Abelian class field theory (ACFT) 399 400 403 ADE algebras 86 ADE groups 289 Adele 399 Adelic 281 ADET Dynkin diagram 113 Adjoint rep 143 Admissible representation 521 AdS/CFT correspondence 304 315 Affine Grassmannian 457 458 481 512 Affine group schemes 633 Affine Hecke algebra 521 Affine Kac-Moody algebra 470 Affine Kac-Moody algebra, chiral algebra 485 Algebra 568 Algebraic closure 397 Algebraic cycle 761 Algebraic group 558 Antipodism 557 568 Arithmetic group 253 262 263 267 269 Arithmetic varieties 340 AS relation 147 Asymptotically free theories 630 Atkin — Lehner involution 382 Attractive abelian variety 226 228 232 238 Attractive K3-surface 224 227 228 232 238 242 334 345 Attractive surface 226 326 Attractor, equations 327 Attractor, mechanism 327 Attractor, points for 342 Attractor, points for exact Calabi — Yau 342 Attractor, varieties 340 Automorphic forms 278 Automorphic function 377 Automorphic representation 404 Automorphic representation, cuspidal 406 408 420 B-field 224 228 230 232—235 239—241 Baker — Campbell — Hausdorff formula 586 Bethe ansatz 68 102 105 Betti number 543 Bialgebra 568 Birdtracks 138 Birdtracks, history 146 Birkhoff decomposition 619 642 661 668 704 Birkhoff — Grothendieck decomposition 644 Black hole entropy 307 315 Black holes 299 Bloch group 15 68 111 761 Bloch group of algebraic numbers 18 19 59 72 Bloch group, extended 110 Bloch group, higher 59 62 Bloch group, torsion elements 37 38 68 Bloch — Wigner function 112 Bogoliubov operation 720 Borel regulator 60 Borel summability 696 Borel transform 696 Borel — Weil — Bott theorem 483 Born — Infeld action 199 202 205 Boundary state 186 188 190 BPHZ renormalization 632 BPS solution 182 BPS state 203 315 328 341 BRS cohomology 700 BRST charge 173 BTZ black holes 316 Calabi — Yau manifold 210 223 Calabi — Yau manifold, four-fold 348 Calabi — Yau manifold, Hodge structure 348 Calabi — Yau manifold, three-fold 305 Calabi — Yau manifold, threefold 384 Calabi — Yau manifold, two-folds, complex structure 225—227 229—231 233 241 Calabi — Yau manifold, two-folds, moduli space 225—227 229 Calabi-Yau theorem 227 Catalan number 769 Center of the chiral algebra 487 Central function 593 CFT see “Conformal Field Theory” Character of conformal field theories see “Conformal Field Theory” Character, Hopf algebra see “Hopf algebra” Chern — Simons invariant 26 73 Chern — Simons theory 317 Chern — Simons theory for supergroup 317 Chevalley group 254 255 262 266 274 Class numbers 336 383 Classical field theory 626 Clifford relations 700 Coadjoint orbits 285 Coalgebra 568 Coassociativity 567 Cohomology, Hochschild see “Hochschild” Coinvariants 472 Comodule 558 Complete monomial function 595 Complex envelope of a compact Lie group 563 Complex spectrum 564 Concatenation product 599 Conformal blocks 471 Conformal field theory 68 Conformal Field Theory, central charge 69 86 113 Conformal Field Theory, character 69 92 Conformal Field Theory, conformal dimensions 69 Conformal Field Theory, minimal model 87 Conformal Field Theory, partition function 70 91 93 Conformal Field Theory, quantum dimension 69 70 Conformal Field Theory, rational 69 344 Congruence subgroup 266 Continued fraction expansion 362 Contragredient representation 557 Controlled pulse universes 367 Convolution product 572 Coproduct 551 Cosmic Galois group 618 623 690 Cosmology 298 Cosmology, BKL model 364 Cosmology, chaotic 361 363 Counterterms see “Renormalization” Coxeter number 86 113 Critical level 484 485 Cuntz — Krieger C*-algebra 370 Cup-product 539 550 Cut-off see “Renormalization” Cyclic category 686 Cyclotomic field 396 D-module 391 432 D-module with regular singularities 435 D-module, holonomic 433 516 D-module, twisted 391 475 478 De Rham cohomology group 543 546 de Rham’s first theorem 546 Decomposition group 401 Decomposition theorem 580 Deconcatenation 599 Dedekind zeta function 16—20 60 Defining rep 136 Defining space 136 Diagrammatic notation 138 Diffeographism 663 Differential Galois group 672 Differential graded algebra 762 763 Dilogarithm 5 6 68 Dilogarithm, enhanced 24 Dilogarithm, finite (dianalog) 31—33 Dilogarithm, functional equations 9 10 34—36 Dilogarithm, identities 37 39 40 Dilogarithm, p-adic 31 33 Dilogarithm, quantum 28—31 Dilogarithm, Rogers 23 73 108 Dilogarithm, special values 7—9 Dim-Reg regularization see “Renormalization” Diophantine conditions 147 149 151 Diophantine conditions, 153 Dirac operator 701 Dirac operator on loop space 310 Dirac quantization 183 202 Divergences see “Renormalization” Divisor function 280 Dp-brane 162 307 Dp-brane, interaction 193 Drinfeld — Sokolov reduction 494 Dual pairs 293 Dual rep 135 Dual space 135 136 143 Dual tensor 141 Dynamical system, chaotic 363 Dynamical system, space of orbits 362 Dyson — Schwinger equations 715 728 Effective action 628 Einstein’s equation 305 Eisenstein series 381 Eisenstein series, adelic representation 281 Eisenstein series, non-holomorphic 278 Elementary symmetric function 595 Elliptic curve 326 Elliptic genus 229 308 Elliptic genus, as Poincar?e series 312 Elliptic genus, for K3 311 Elliptic genus, for symmetric products 310 Enveloping algebra 570 Euler — Zagier sums 602 706 743 748 Exceptional Lie algebra see “Lie algebra” Exceptional magic 153 Exceptional magic, history 154 Expansional formula 651 660 689 Exponents 544 F-theory 344 347 Faber polynomials 374 381 385 Fermat quartic in 223—225 227 228 230 233 235 237 240—242 Fermat’s Last Theorem 406 413 Feynman diagrams 138 147 156 157 627 Feynman graphs 620 Feynman loop integral 737 749 Feynman loop integral, propagator 629 Feynman loop integral, regularisation 740 Feynman loop integral, scalar integrals 740 Feynman parameters 740 Five-term relation 15 33—36 Flat connection 425 Flat connection, holomorphic 426 Flat equisingular bundles 691 Forest see “Plane tree” Forest, cycling map 768 Forest, R-deco 764 Fourier — Mukai transform 448 449 Fourier — Mukai transform, non-abelian 464 502 517 Free Abelian group 109 Free fermion 78 Free group 259 264 265 Frobenius automorphism 400 Frobenius automorphism, geometric 403 417 Fuchs criterion 667 Function field 414 Fundamental group 417 425 Galois group 396 Gauge/gravity correspondence 204 Gaugino condensate 218 Gauss density 366 Gaussian 282 Gaussian measure 627 Gel’fand — Kirillov dimension 285 Generating function 627 Geodesic on modular curve 365 Geometric Langlands correspondence 390 439 462 517 520 Gepner model 223 224 230 232 233 235 241 242 312 Global nilpotent cone 516 Green’s function 626 Green’s function, connected 628 Green’s functions, relation to polylogarithms 12 Grothendieck fonctions-faisceaux dictionary 429 Grothendieck — Teichmuller group 623 Group theoretic weight, QCD 134 Group theoretic weight, SU(n) 146 Group, general linear 135 Group, invariance 134 136 137 147—149 157 Group, Lie 135 GSO projection 168 192 H-space 551 Harish — Chandra pair 407 478 Hecke correspondence 436 Hecke eigensheaf 390 438 439 443 461 462 502 508 516 519 522 Hecke functor 438 Hecke operator 377 410 421 437 438 Hitchin system 469 515 Hochschild, cohomology 715 721 724 Hochschild, cohomology, renormalizability 726 Hochschild, one-cocycles 718 Hodge structure of Calabi — Yau manifold 304 Homology 542 Hopf algebra 568 633 737 742 753 770 Hopf algebra of nested sums 746 Hopf algebra, character 719 Hopf algebra, decorated rooted trees 620 635 724 Hopf algebra, renormalization 715 Hopf’s Theorem 553 Hyperbolic 3-manifolds 13—15 26 Hypergeometric function 747 Hyperkahler resolution 307 Hyperkahler structure 224 227 228 240 242 IHX relation see “Jacobi relation” Index formula 623 Inertia group 401 Infinitesimal transformation 143 Infrared divergences 638 Integrable system 704 Intersection cohomology sheaf 457 Invariance group 134 136 137 147—149 157 Invariant, primitive 136 139 141 147 Invariant, primitive, 148 Invariant, tensor 137 Invariant, tensor, SO(3) 139 Invariant, tensor, SU(n) 142 Iterated integral for multiple polylogarithm 760 Jacobi relation 145 147 150 K-theory, algebraic 18 19 59 60 62 63 67 106 K-theory, torsion elements 38 67 K3-surface 315 K3-surface, attractive 224 227 228 238 242 K3-surface, lattice polarized 235 236 K3-surface, very attractive 223 224 227 238—242 Kac — Moody Lie algebra 82 84 Kahler class 227 228 231 233 239 240 Kahler structure 345 Kaluza — Klein states 183 Kasner metric 363 Killing spinor equation 210 Kirillov — Kostant symplectic form 283 KK-theory 686 KMS condition 370 KMS states 370 371 Kronecker delta 135 Kummer lattice 237 Kummer surface 232 236—238 240 l-adic representation 418 l-adic sheaf 429
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