668
Index
Spinless Salpeter equation, 102
Spin matrices, 62
Spin–orbit corrections, 362
Spin–orbit coupling, 360, 361, 364–365
Spin-s representation, 61–62
Spintronics, 309
Spin-valued linear problems, 40–41
geometric interpretation, 41
soliton surfaces approach, 41
Spin-valued spectral problems, 38
Square lattice, evolution, 28–29
Squeezed states
1D Harmonic oscillator, 256–257
SU(2) coherent states, 258–260
2D, 260–262
2D isotropic oscillator, 257–258
SrTiO 3 , 360
Stable negative mass de sitter bubbles, 477–478
Standard Big Bang cosmology, 409
Standard model (SM), 557, 567, 575, 579–581,
597
gauge groups, 598
loop-induced processes, 598
Yukawa couplings, 599
Standard Model of Particle Physics (SM), 417,
418, 427
Star proper length, 503
Static lattice, 312, 313
Static Newtonian force, 472
Statistical mechanics, 4
Stellar objects, 572
Stochastic Burgers equation, 528
Stochastic differential equations (SDEs), 522
Stochastic heat equation, 529
Stokes parameters, 570–573
Stress-energy tensor, 476
String gas cosmology, 411, 412
String theory, 409
SU(2) coherent states, 258–260
Super-A-polynomials
quantum, 278
and volume conjectures, 283–284
Superconductivity
Coulomb repulsion, 365, 366
electron-phonon coupling, 359
Luttinger semimetals, 360, 362–364
semiconductors, 360
Superconformal mechanics (SCM), 200
Superconformal quantum mechanics, 199
Superfluid dark matter
BEC, 439
Broglie wavelength, 439
conditions, 439
Galilean symmetry, 439
MOND, 439
phonon-mediated acceleration, 440
polytropic equation, 439
Super-Hubble fluctuations, 410
Superintegrable Higgs algebra, 176
Super-Planckian, 441
Super-Poincaré algebra, 199
Superpolynomials, 277
asymptotic expansion, 282
categorified, 278
trefoil, 282
twist knots, 278, 281, 282
Superstring theory, 413
Supersymmetric quantum mechanics (SUSY
QM), 47–49, 121
complex oscillator, 52–53
definition, 199
first-order, 265
Hamiltonians, 235
and nonlinear algebras, 235
second-order, 236–238, 265, 268–269
Zn2-graded color superalgebra, 200, 201
Supersymmetric spin models
chemical potential, 14
exchange operator, 13
partition functions, 14–15
Su–Schrieffer–Heeger (SSH), 632
Sutherland model, 147
Swampland, 448, 449
Swampland criteria, 413
Symmetries
five points symmetries, 30
heavy diquark and quark spin flavor
symmetry (see Heavy diquark and
quark spin flavor symmetry)
inflationary cosmology (see Inflationary
cosmology)
Lax pair, 30
scale invariance (see Scale invariance)
three points symmetries, 29
Sym’s (or Sym-Tafel) formula, 41
T
Tachyonic representations, see Representation
theory
T -duality symmetry, 414
Tensor-to-scalar ratio, 419
Test function, 362
Thermodynamics, 17–18
su(1|1) case, 18–19
Thin wall bubbles, 476
Third order superintegrability, 114–115
3D consistency, 30, 33
Index
Spinless Salpeter equation, 102
Spin matrices, 62
Spin–orbit corrections, 362
Spin–orbit coupling, 360, 361, 364–365
Spin-s representation, 61–62
Spintronics, 309
Spin-valued linear problems, 40–41
geometric interpretation, 41
soliton surfaces approach, 41
Spin-valued spectral problems, 38
Square lattice, evolution, 28–29
Squeezed states
1D Harmonic oscillator, 256–257
SU(2) coherent states, 258–260
2D, 260–262
2D isotropic oscillator, 257–258
SrTiO 3 , 360
Stable negative mass de sitter bubbles, 477–478
Standard Big Bang cosmology, 409
Standard model (SM), 557, 567, 575, 579–581,
597
gauge groups, 598
loop-induced processes, 598
Yukawa couplings, 599
Standard Model of Particle Physics (SM), 417,
418, 427
Star proper length, 503
Static lattice, 312, 313
Static Newtonian force, 472
Statistical mechanics, 4
Stellar objects, 572
Stochastic Burgers equation, 528
Stochastic differential equations (SDEs), 522
Stochastic heat equation, 529
Stokes parameters, 570–573
Stress-energy tensor, 476
String gas cosmology, 411, 412
String theory, 409
SU(2) coherent states, 258–260
Super-A-polynomials
quantum, 278
and volume conjectures, 283–284
Superconductivity
Coulomb repulsion, 365, 366
electron-phonon coupling, 359
Luttinger semimetals, 360, 362–364
semiconductors, 360
Superconformal mechanics (SCM), 200
Superconformal quantum mechanics, 199
Superfluid dark matter
BEC, 439
Broglie wavelength, 439
conditions, 439
Galilean symmetry, 439
MOND, 439
phonon-mediated acceleration, 440
polytropic equation, 439
Super-Hubble fluctuations, 410
Superintegrable Higgs algebra, 176
Super-Planckian, 441
Super-Poincaré algebra, 199
Superpolynomials, 277
asymptotic expansion, 282
categorified, 278
trefoil, 282
twist knots, 278, 281, 282
Superstring theory, 413
Supersymmetric quantum mechanics (SUSY
QM), 47–49, 121
complex oscillator, 52–53
definition, 199
first-order, 265
Hamiltonians, 235
and nonlinear algebras, 235
second-order, 236–238, 265, 268–269
Zn2-graded color superalgebra, 200, 201
Supersymmetric spin models
chemical potential, 14
exchange operator, 13
partition functions, 14–15
Su–Schrieffer–Heeger (SSH), 632
Sutherland model, 147
Swampland, 448, 449
Swampland criteria, 413
Symmetries
five points symmetries, 30
heavy diquark and quark spin flavor
symmetry (see Heavy diquark and
quark spin flavor symmetry)
inflationary cosmology (see Inflationary
cosmology)
Lax pair, 30
scale invariance (see Scale invariance)
three points symmetries, 29
Sym’s (or Sym-Tafel) formula, 41
T
Tachyonic representations, see Representation
theory
T -duality symmetry, 414
Tensor-to-scalar ratio, 419
Test function, 362
Thermodynamics, 17–18
su(1|1) case, 18–19
Thin wall bubbles, 476
Third order superintegrability, 114–115
3D consistency, 30, 33