Index
667
de Sitter group, 131
Hermitian matrix, 642
Lie algebra homomorphism, 137
quantum formalism, 641
SDP relaxations, 641
skew symmetric translation generators, 138
SO 0 (2, 3), Sp(2,R), Poincaré group/lie
algebras, 132–134
Sp(2,R), 136
Riccati equation, 237
Ricci scalar, 419
Ricci tensor, 466
Riemann sphere, 79
Riemann tensor, 466
Right-handed neutrino, 589
Right-handed W R boson mass, 587
S
Salpeter equation, 101
solutions, 103–104
Scalar field, 543
Scale invariance
de Sitter space time, 543–545
Dirac delta function, 544
energy density perturbations, 544
free quantum field theory, 545
galaxy power spectrum, 547–459
Minkowski space time, 544
non-Gaussianity, 547–459
power spectrum, 545
Scaling dimension
fermion bilinear, 342–343
monopole operator, 329–332
Schrödinger equation, 101, 112, 237, 238, 257,
295–298, 300, 634
Schwarzschild-de Sitter metric, 476
Schwinger boson, 258
Second-degree PHA, 50–51
Second-order difference equations, 67
Second-order differential operator, 268
Second-order perturbation theory, 310
Second-order SUSY partners, 268
TRM potentials, 239–242
Second-order SUSY QM, 236–238
and constant magnetic field, 270, 271
eigenfunctions, 269, 271
eigenvalues, 269, 271
and functions, 272
harmonic oscillators, 270
magnetic fields, 272, 273
Schrödinger Hamiltonians, 268
Second-order symmetry operator, 113
Second-order transformations, 237
Self-organization, 499, 505
Semiconductors, EPI, 308
Semimetal-to-Kekulé-VBS transition, 342
Sequential Standard Model (SSM), 557
Short-ranged four-fermion interaction, 340
Shubnikov–de Haas oscillations, 312
Sigma models, 58
analytical solutions, 59–61
Simple Lie algebras
characters, 287
and homogeneous spaces, 3
Littlewood–Richardson rule, 288
Single-site entropies, 350
Singularities, 31–32
Singularity analysis, 26–27
Singular vectors, 221
sl(3) black holes
conformal invariance, 402
entropy bounds, 402
extremality vs. unitarity, 401–402
finite entropy, 401
Jordan classes, 401
Jordan decomposition vs. zero temperature,
400–401
supersymmetry and extremality, 402
Slow-roll inflation models, 413
Small neutrino masses, 585
SM-DM couplings, 427
Smooth cigar-like geometry, 394
Smoothness condition, 395, 397
SM radiation, 431
Soliton solution, vmKdV hierarchy
breather solution, 517–519
Darboux transformation, 514, 519
dressing and Bäcklund transformation,
515–516
Lax–Darboux equations, 514
Lax operator, 514, 519
linear equations, 514
rational dressing, 514
Solvable potentials
case with j=0, 270–271
case with j =0, 271–273
Space-memory, 103
Space quantization, 372
Space-time, 500, 501
SPDEs, 528–529
Spectral action, 247
Spin-3 chemical potential, 397, 400
Spin dynamical models, 6–7
A N −1 spin Calogero model, 7–9
coordinate permutation operators, 7
Dunkl operators, 8
Spin-Hall mass, 330–332
667
de Sitter group, 131
Hermitian matrix, 642
Lie algebra homomorphism, 137
quantum formalism, 641
SDP relaxations, 641
skew symmetric translation generators, 138
SO 0 (2, 3), Sp(2,R), Poincaré group/lie
algebras, 132–134
Sp(2,R), 136
Riccati equation, 237
Ricci scalar, 419
Ricci tensor, 466
Riemann sphere, 79
Riemann tensor, 466
Right-handed neutrino, 589
Right-handed W R boson mass, 587
S
Salpeter equation, 101
solutions, 103–104
Scalar field, 543
Scale invariance
de Sitter space time, 543–545
Dirac delta function, 544
energy density perturbations, 544
free quantum field theory, 545
galaxy power spectrum, 547–459
Minkowski space time, 544
non-Gaussianity, 547–459
power spectrum, 545
Scaling dimension
fermion bilinear, 342–343
monopole operator, 329–332
Schrödinger equation, 101, 112, 237, 238, 257,
295–298, 300, 634
Schwarzschild-de Sitter metric, 476
Schwinger boson, 258
Second-degree PHA, 50–51
Second-order difference equations, 67
Second-order differential operator, 268
Second-order perturbation theory, 310
Second-order SUSY partners, 268
TRM potentials, 239–242
Second-order SUSY QM, 236–238
and constant magnetic field, 270, 271
eigenfunctions, 269, 271
eigenvalues, 269, 271
and functions, 272
harmonic oscillators, 270
magnetic fields, 272, 273
Schrödinger Hamiltonians, 268
Second-order symmetry operator, 113
Second-order transformations, 237
Self-organization, 499, 505
Semiconductors, EPI, 308
Semimetal-to-Kekulé-VBS transition, 342
Sequential Standard Model (SSM), 557
Short-ranged four-fermion interaction, 340
Shubnikov–de Haas oscillations, 312
Sigma models, 58
analytical solutions, 59–61
Simple Lie algebras
characters, 287
and homogeneous spaces, 3
Littlewood–Richardson rule, 288
Single-site entropies, 350
Singularities, 31–32
Singularity analysis, 26–27
Singular vectors, 221
sl(3) black holes
conformal invariance, 402
entropy bounds, 402
extremality vs. unitarity, 401–402
finite entropy, 401
Jordan classes, 401
Jordan decomposition vs. zero temperature,
400–401
supersymmetry and extremality, 402
Slow-roll inflation models, 413
Small neutrino masses, 585
SM-DM couplings, 427
Smooth cigar-like geometry, 394
Smoothness condition, 395, 397
SM radiation, 431
Soliton solution, vmKdV hierarchy
breather solution, 517–519
Darboux transformation, 514, 519
dressing and Bäcklund transformation,
515–516
Lax–Darboux equations, 514
Lax operator, 514, 519
linear equations, 514
rational dressing, 514
Solvable potentials
case with j=0, 270–271
case with j =0, 271–273
Space-memory, 103
Space quantization, 372
Space-time, 500, 501
SPDEs, 528–529
Spectral action, 247
Spin-3 chemical potential, 397, 400
Spin dynamical models, 6–7
A N −1 spin Calogero model, 7–9
coordinate permutation operators, 7
Dunkl operators, 8
Spin-Hall mass, 330–332