662
Index
Higher spin gravity
AdS 3 , 391–392
AdS/CFT correspondence, 390
black holes (see Euclidean black holes;
Extremal black holes)
features, 389
puzzling, 389
Wilson lines, 402–406
Higher spin theories, 389
Hilbert–Schmidt inner product, 250
Hilbert space, 257, 280, 318
Hodgkin–Huxley model, 150
Holographic radial direction, 392
Holomorphic black hole, 396
Holonomy conditions, 404
Homogeneous field variance, 419
Honeycomb lattice, 342
Horizon and flatness problems, 409
Hubble radius, 411
Hypotheses
algorithms, 629
causal intermediary, 627
cause and effect, 628
variables, 627
I
IIB compactification, 448
Inflation, 419
Inflationary cosmology, 413, 415, 543
CMB anisotropy, 545–547
coordinate space, 547
density perturbations, 546
de Sitter space, 546
Harrison–Zeldovich spectrum, 545
mass density, 545
non-Gaussianities, 546, 547
potential energy, 543
QSFI, 547
quantum fluctuations, 544, 545
Inflationary reheating model, 431
Inflationary scenario, 409
Infrared spectroscopy, 312
Integrability, 68–70
Integrability indicators, 69
Integrable fourth-order difference equation,
67
Integrable systems, 4, 511
Intensity mapping (IM)
astrophysical phenomena, 458
astrophysics, 458
cosmology, 457
inter-relationship (see Cosmology and
astrophysics inter-relationship)
large-scale structure, 457
surveys, 458
Interstellar medium (IM), 458
Intraband and interband couplings, 310–311
Invariant operator, 296
Ishibashi state, 406
Isocurvature perturbations, 423
Isometries, 38–39
Itinerant ferromagnetism, 482, 485
J
Jacobi algebra
case G2, 219
definition, 217
triangular decomposition, 218
Jacobi orthogonal polynomials, 146, 147
J -matrix, 350
Jones polynomial
asymptotic behavior, 277
categorification, 276
structure, 277
twist knots, 282
K
Kähler angles, 65
Kerr–Newman black holes, 373
Khovanov polynomial, 276
Knot homology, 276
Knot invariants
and CS theory, 276, 279–281
integrality structure, 276
quantum, 277
Kohn–Luttinger mechanisms, 363
Kolmogorov backward equation, 522
Krawtchouk orthogonal polynomials, 60
Kruskal gauge, 404
L
Ladder operators
categorical structure, 126–127
examples, 129
harmonic oscillator, 122
Maya diagrams, 122–123, 127, 128
rational extensions, 122, 124–125
Lagrange inversion theorem and analysis
compensating mass, 470, 472
conserve momentum, 471
dimensionless instantaneous time, 469
dynamical effects, 468
energy-momentum, 470
final expression, 472
Index
Higher spin gravity
AdS 3 , 391–392
AdS/CFT correspondence, 390
black holes (see Euclidean black holes;
Extremal black holes)
features, 389
puzzling, 389
Wilson lines, 402–406
Higher spin theories, 389
Hilbert–Schmidt inner product, 250
Hilbert space, 257, 280, 318
Hodgkin–Huxley model, 150
Holographic radial direction, 392
Holomorphic black hole, 396
Holonomy conditions, 404
Homogeneous field variance, 419
Honeycomb lattice, 342
Horizon and flatness problems, 409
Hubble radius, 411
Hypotheses
algorithms, 629
causal intermediary, 627
cause and effect, 628
variables, 627
I
IIB compactification, 448
Inflation, 419
Inflationary cosmology, 413, 415, 543
CMB anisotropy, 545–547
coordinate space, 547
density perturbations, 546
de Sitter space, 546
Harrison–Zeldovich spectrum, 545
mass density, 545
non-Gaussianities, 546, 547
potential energy, 543
QSFI, 547
quantum fluctuations, 544, 545
Inflationary reheating model, 431
Inflationary scenario, 409
Infrared spectroscopy, 312
Integrability, 68–70
Integrability indicators, 69
Integrable fourth-order difference equation,
67
Integrable systems, 4, 511
Intensity mapping (IM)
astrophysical phenomena, 458
astrophysics, 458
cosmology, 457
inter-relationship (see Cosmology and
astrophysics inter-relationship)
large-scale structure, 457
surveys, 458
Interstellar medium (IM), 458
Intraband and interband couplings, 310–311
Invariant operator, 296
Ishibashi state, 406
Isocurvature perturbations, 423
Isometries, 38–39
Itinerant ferromagnetism, 482, 485
J
Jacobi algebra
case G2, 219
definition, 217
triangular decomposition, 218
Jacobi orthogonal polynomials, 146, 147
J -matrix, 350
Jones polynomial
asymptotic behavior, 277
categorification, 276
structure, 277
twist knots, 282
K
Kähler angles, 65
Kerr–Newman black holes, 373
Khovanov polynomial, 276
Knot homology, 276
Knot invariants
and CS theory, 276, 279–281
integrality structure, 276
quantum, 277
Kohn–Luttinger mechanisms, 363
Kolmogorov backward equation, 522
Krawtchouk orthogonal polynomials, 60
Kruskal gauge, 404
L
Ladder operators
categorical structure, 126–127
examples, 129
harmonic oscillator, 122
Maya diagrams, 122–123, 127, 128
rational extensions, 122, 124–125
Lagrange inversion theorem and analysis
compensating mass, 470, 472
conserve momentum, 471
dimensionless instantaneous time, 469
dynamical effects, 468
energy-momentum, 470
final expression, 472