Index
665
polyatomic molecules, 318
probability density, 321–325
strain, 321
2DDMs, 317–325
Nonlinear defining equations, 115–119
Nonlinear power spectrum, 459
Non-linear QED, 569
Nonlocal operator, 104–107
Non-minimal coupling, 423
Non-perturbative terms decouple, 449
Non-self-adjoint operators, 521
Nonstationary oscillator, 296
time-dependent mass, 296–297
Non-trivial phases, 307–308
Normalization, 379
Numerical computation, 352
O
1D Harmonic oscillator, 256–257
1D ladder operators, 258, 261
One-dimensional Schrödinger Hamiltonians,
236
One-soliton solution, 516
Optimal classical strategy
error probability, 622
Organic conductors, 317
Oscillators, 372
P
Painlevé IV (PIV) equation, 47
Parametric oscillator, 296
Partial differential equations (PDE)
application, 149
definition, 149
discretized equation, 153–155
lie-point symmetries, 150
reaction diffusion models, 150
symmetry reduction and discretization,
case, 151–153
Partial differential equations in curved spaces
elementary function, 494
homogeneous version, 493, 494
matrix inversion, 498
Maxwell’s equations, 495
orthonormal eigenvectors, 496
time-independent solutions, 496
2 + 1 and 3 + 1 dimensions, 491, 492, 494
Whittaker’s method, 491, 495
Partial differential operators, 114
Particle mass spectrum, 562
Partition functions, 11–12, 14–15, 380
Parton distribution function (PDF), 559
Pauli matrices, 250, 251, 328, 329, 339
Pearcey equation, 103, 108
Perlick’s II system, 141
Phases resides, 307
Phenomenology
DM decay, 422–424
Higgs-portal scalar field, 424
Phonon-based pairing, 366
Phonon-induced gap renormalization, 312–314
Phonon-induced topological insulation,
308–309
Phonons, 439
Photon spectrum, 568
Physical degrees of freedom, 377–379
Physical/non-physical solutions, 237
PIV transcendents, 53–54
Planck satellite, 432
Planck units, 412
Point transformations
complex-valued function, 299
Ermakov equation, 300
invariant operator, 302
nonstationary oscillator, 300
orthogonal set of solutions, 301–302
parametric oscillator, 300
real-valued functions, 299, 300
Schrödinger equation, 298, 300
stationary oscillator, 302
subindex notation, 298
time-dependent complex-phase, 302
Poisson algebra (PA), 182
Poisson brackets, 377
Poisson vertex algebra (PVA), 182
Polychronakos–Frahm (PF) spin chain, 10
Polynomial Heisenberg algebras (PHA), 49
second-degree, 50–51
Polytope expansion, 290
Pre-Big-Bang scenario, 411
Primordial non-Gaussianity, 462, 463
Probability density, 321–325
Projector formalism, 58–59
Prokushkin–Vasiliev higher spin theory, 390
Pseudo-Euclidean space, 39
Q
QED 3 -cHGN quantum critical point (QCP)
characterize, 329
monopole operator, 331, 333
QED 3 -GN models, 335
SU(6) decomposes, 334
QED 3 -Gross–Neveu (GN) model, 327–335,
338, 340, 341, 343, 344
QED 3 Lagrangian, 339
665
polyatomic molecules, 318
probability density, 321–325
strain, 321
2DDMs, 317–325
Nonlinear defining equations, 115–119
Nonlinear power spectrum, 459
Non-linear QED, 569
Nonlocal operator, 104–107
Non-minimal coupling, 423
Non-perturbative terms decouple, 449
Non-self-adjoint operators, 521
Nonstationary oscillator, 296
time-dependent mass, 296–297
Non-trivial phases, 307–308
Normalization, 379
Numerical computation, 352
O
1D Harmonic oscillator, 256–257
1D ladder operators, 258, 261
One-dimensional Schrödinger Hamiltonians,
236
One-soliton solution, 516
Optimal classical strategy
error probability, 622
Organic conductors, 317
Oscillators, 372
P
Painlevé IV (PIV) equation, 47
Parametric oscillator, 296
Partial differential equations (PDE)
application, 149
definition, 149
discretized equation, 153–155
lie-point symmetries, 150
reaction diffusion models, 150
symmetry reduction and discretization,
case, 151–153
Partial differential equations in curved spaces
elementary function, 494
homogeneous version, 493, 494
matrix inversion, 498
Maxwell’s equations, 495
orthonormal eigenvectors, 496
time-independent solutions, 496
2 + 1 and 3 + 1 dimensions, 491, 492, 494
Whittaker’s method, 491, 495
Partial differential operators, 114
Particle mass spectrum, 562
Partition functions, 11–12, 14–15, 380
Parton distribution function (PDF), 559
Pauli matrices, 250, 251, 328, 329, 339
Pearcey equation, 103, 108
Perlick’s II system, 141
Phases resides, 307
Phenomenology
DM decay, 422–424
Higgs-portal scalar field, 424
Phonon-based pairing, 366
Phonon-induced gap renormalization, 312–314
Phonon-induced topological insulation,
308–309
Phonons, 439
Photon spectrum, 568
Physical degrees of freedom, 377–379
Physical/non-physical solutions, 237
PIV transcendents, 53–54
Planck satellite, 432
Planck units, 412
Point transformations
complex-valued function, 299
Ermakov equation, 300
invariant operator, 302
nonstationary oscillator, 300
orthogonal set of solutions, 301–302
parametric oscillator, 300
real-valued functions, 299, 300
Schrödinger equation, 298, 300
stationary oscillator, 302
subindex notation, 298
time-dependent complex-phase, 302
Poisson algebra (PA), 182
Poisson brackets, 377
Poisson vertex algebra (PVA), 182
Polychronakos–Frahm (PF) spin chain, 10
Polynomial Heisenberg algebras (PHA), 49
second-degree, 50–51
Polytope expansion, 290
Pre-Big-Bang scenario, 411
Primordial non-Gaussianity, 462, 463
Probability density, 321–325
Projector formalism, 58–59
Prokushkin–Vasiliev higher spin theory, 390
Pseudo-Euclidean space, 39
Q
QED 3 -cHGN quantum critical point (QCP)
characterize, 329
monopole operator, 331, 333
QED 3 -GN models, 335
SU(6) decomposes, 334
QED 3 -Gross–Neveu (GN) model, 327–335,
338, 340, 341, 343, 344
QED 3 Lagrangian, 339