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Ambjorn J., Durhuus B., Jonsson T. — Quantum Geometry. A Statistical Field Theory Approach
Ambjorn J., Durhuus B., Jonsson T. — Quantum Geometry. A Statistical Field Theory Approach

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Название: Quantum Geometry. A Statistical Field Theory Approach

Авторы: Ambjorn J., Durhuus B., Jonsson T.

Аннотация:

This graduate level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantization of strings, gravity and topological field theory. With chapters on random walks, random surfaces, two-and higher-dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach uses discrete approximations and develops analytical and numerical tools. Continuum physics is recovered through scaling limits at phase transition points and the relation to conformal quantum field theories coupled to quantum gravity is described. The most important numerical work is covered, but the main aim is to develop mathematically precise results that have wide applications. Many diagrams and references are included.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 374

Добавлена в каталог: 06.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$b$-loop functions      71
$b$-point function      83
$n$-point function      55
$q$-analogues      334
$q$-dimension      334
6$j$-symbols      315 323 325 328
Abstract triangulation      276
Adjacency matrix      85
Alexander moves      284
Algorithm      286
Algorithmic classifiability      274 286
Algorithmic decidability      286
Algorithmic recognizability      284 286
Angular momentum operator      53
Annealed average      137 238
Anomalous dimension      44 60 102 122 215 223
Area of lattice surface      107
Asymptotic expansion      211
Asymptotic safety      273
Average distance      63
Average internal length      43
Axioms      298
Baby universe      242 265
Baby universe surgery      291
Bare cosmological constant      155
Biedenharn — Elliott — Racah identities      316 329
Boltzmann factor      14 238
Bottlenecks      117 240
Boundary      74 107
Boundary link      106
Branched polymer dominance      103
Branched polymer model      94
Branched polymers      8 53 54 90 93 242 293
Brownian motion      11 45
Canonical partition function      131
Cayley tree      294
Central charge      193 195
Checker board polygons      230
Chern classes      236
Chern — Simons theory      7 273 297 312 336
Clebsch — Gordan coefficients      324
Clifford algebra      46 51 52
Closed triangulations      178
Cluster algorithms      254
Co-associativity      335
Co-product      334
Combinatorial equivalence      277
Combinatorial Laplacian      78
Combinatorial manifold      277
Combinatorial triangulation      73
Combinatorial unitarity      71
Commutative $*$-algebra      307
Compatibility      278
computer simulations      251
Conformal factor      94
Conformal weight      193
Connected lattice surface      107
Continuum distance      214
continuum limit      102 182
Continuum loop equation      199 204
Continuum loop functions      84
Continuum mass      214
Continuum propagator      214
Cosmological constant      19 149 150 182
Counting problem      165
Critical coupling      79
critical exponent      23 31 44 60 62 260
Critical exponent of mass      110
Critical exponent of string tension      114
Critical exponent of susceptibility      112
Critical hyper-surfaces      197
Critical slowing down      254
Crumpling transition      130 135 143 147
Crystalline membranes      147
Crystalline surface model      137
Curvature assignments      281
Curvature-dependent action      32
Deficit angle      76 279
Deligne — Knudsen — Mumford compactification      236
Detailed balance      252
Diffeomorphism classes      279
Diffeomorphism invariance      299
Diffusion equation      12
Dimensionless mass      30
Dimensionless propagator      30
Dimer model      191
Dirac operator      46
Dirac propagator      48 52 53
Direct sum of TQFTs      302
Discrete approximation      15
Discretized extrinsic curvature action      127
Distance      61
Donsker’s theorem      16
Double scaling limit      183 189 233
Dressed scaling dimension      197
DTRS-model      68
Dual graph to a triangulation      75
Dual lattice      212
Dynamically triangulated random surface model      68
Dyson — Schwinger equation      247
Effective rigidity      53
Eigenvalue density      231
Einstein — Hilbert action      3 149 271 284
Embedding of a branched polymer      54
Entrance loop      216
entropy      21
Entropy exponent      154 186
Ergodicity      252
Euclidean Chern — Simons gravity      315
Euclidean space      271
Euclidean string theory      270
Euler characteristic      71 107 227 274
Euler’s formula      72
Excess angle      76
Exit loop      216
expectation value      237 252
Extrinsic curvature      32 125
Extrinsic curvature coupling      34 127
Extrinsic Hausdorff dimension      100
Factorization      299
Fermionic random walk      47
Field redefinitions      230
Finite-size scaling      260
Finitely presented groups      287
Fisher’s scaling relation      44 63 102 215
Flip      255 258
Fluid membranes      137 147
Free energy      260
Frobenius algebra      302 310
Fugacity      193
Functional integral formalism      297
Fundamental form      32
Gauss — Bonnet formula      72
Gaussian action      24
Gelfand — Dikii polynomials      209
General covariance      297
Generalized loop equation      175
Generalized matrix models      282
Generating functions      157 169
Geodesic distance      101 212
Geodesic triangle      75
Geodesic two-loop function      216
Geometric path      2 19 20
Geometric random walks      19
Geometric surfaces      3
Gibbs free energy      96 131
Gluing property      321
Hamiltonian formalism      249
Hard dimer problem      191
Hartle — Hawking wave functional      150 155 185
Hausdorff dimension      42 43 61 100 139 152 222 291
Heat kernel      12
Helmholtz free energy      131
Hermitian matrix model      234
Hexatic membranes      147
Hyper-scaling      263
Imaginary magnetic field      193
Indecomposable TQFTs      302
Inhomogeneous Lorentz group      311
Interior vertices      70
Intersection indices      236
Intertwiner      324
Intrinsic anomalous dimension      62
Intrinsic Hausdorff dimension      61 101 293
Intrinsic mass      62
Intrinsic physical mass      62
Intrinsic susceptibility      63
Intrinsic two-point function      61
Irreducible surface      116
Ising model      192 238
Isomorphic triangulations      75
KdV-hierarchy      199 209
Kontsevich model      234
Korteweg-de Vries hierarchy      199
Labelled triangulations      256
Laplace — Beltrami operator      38
Lattice Laplacian      22
Lattice loop      107
Lattice path      20
Lattice propagator      22
Lattice random surface model      68
Lattice surface      105 106
Lee — Yang edge singularity      193 239
Link      54 105 106
Loop equation      160 175
Loop function      79 107 155
Loop insertion operator      167 201 235
Lorentzian space-time      271
LRS-model      68 104
Magnetic field      193
Majorana field      239
Marinari — Parisi model      249
Markov chain      252
Mass      95 110
Massive scaling limits      199
Matrix models      226
Mean curvature      125
Mean field theory      90 241
Mean-square extent      43 100
Mermin — Wagner theorem      143
Metric structure      278
Metropolis algorithm      254
Metropolis updating      253
Minimal baby universes      242
Minimal conformal field theory      240
Minkowski space      273
Modified adjacency matrix      85
Moments      171
Moments $M_{k}$ and $J_{k}$      165
Monte Carlo methods      270
Monte Carlo simulations      251 289
Moves      254 284 317
Multi-critical hyper-surface      190
Multi-critical models      189 198
Multi-loop functions      181 235
Multiple Ising system      246
Nambu — Goto action      66
Nilpotent elements      310
Non-perturbative regularization      233
One-dimensional gravity      19
Order of simplexes      279
Order of vertices      54
Ornstein — Uhlenbeck process      45
Osterwalder — Schrader axioms      271
Osterwalder — Schrader positivity      146
Painleve equation      210 233
Parameter manifold      71
Parametrized piecewise linear paths      12
Parametrized random surface theory      139
Partition function      80 252 309
Peeling      218
Persistence length      141
Physical mass      103
Physical string tension      103
Piecewise linear manifold      69
Piecewise linear structures      278
Piecewise linear surface      70 73 75
Piecewise linear topology      277
PL-manifold      278
Planar branched polymer      54
Planar lattice random surfaces      107
plaquette      105 106
PLRS-model      107
Pockets      213
Polyakov action      67 72
Polyakov string theory      270
POLYGONS      166
Ponzano — Regge construction      338
Pre-string equation      205
Primary fields      195
Propagator      18
Pseudo-critical point      260
Pseudo-manifolds      276
Puncture      83 186
Quantum deformations      333
Quantum geometry      263
Quantum gravity      271
Quantum universe      294
Quenched average      238
Radius of gyration      100
Random walk representation      13
Reduced one-point function      56
Reduced tensor product      335
Regge calculus      6 68 73
Regular triangulations      156 277
Regularized propagator      30
Relevant eigenvalues      262
Renormalization      182
Renormalization group      18 61 262
Renormalized gravitational coupling      188
Reparametrization      19
Reparametrization invariance      2
Reparametrization invariant measure      19 20
Reshetikhin — Turaev invariants      337
Riemann surfaces      236
Riemannian curvature tensor      274
Riemannian random walks      24
Riemannian structure      279
Rigid random walk      32 45
Scalar curvature      272
Scale transformation      34
Scaling ansatz      262
Scaling dimension      196 261
Scaling limit      122 238
Scaling relations      260
Schr$\ddot{o}$dinger equation      209
Schr$\ddot{o}$dinger representation      300
Second fundamental form      125
Self-avoiding random walks      65
Signature      274
Simplicial complex      275
Simplicial quantum gravity      275
Singlet representation      325
Slicing      218
Spanning property      309
Spanning tree      80
Specific heat      134 262
Spin operator      53
Spin susceptibility      262
Statistical mechanics      251
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