Cartier P., Julia B., Moussa P. — Frontiers in Number Theory, Physics, and Geometry II :: Электронная библиотека попечительского совета мехмата МГУ

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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 II

Авторы: 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.

More than ten years after a first meeting in 1989 between number theorists and physicists at the Centre de Physique des Houches, a second 2-week event focused on the broader interface of number theory, geometry, and physics.

This book is the result of that exciting meeting, and collects, in 2 volumes, extended versions of the lecture courses, followed by shorter texts on special topics, of eminent mathematicians and physicists.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 789

Добавлена в каталог: 07.05.2008

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Предметный указатель

family      148
family      134 153 155
family      150
family      153
$GL(n,\mathbb{C})$       135
family      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, family      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 $\mathbb{C}\mathbb{P}^3$       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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