666
Index
Quad equation, 22–23
algebraic entropy, 28
CAC, 24
discrete Lax pairs, 23–24
Lax pair from CAC, 24–25
singularity structure, 26–27
square lattice, evolution, 28–29
symmetries, 25–26
vertical/horizontal symmetries (see
Symmetries)
Quantum advantages
coherence, 622
random variables, 622
Quantum affine W-algebra, 181
Quantum canonical transformation, 523
Quantum causal models, 616
Quantum computing, 309
Quantum corrections, 448
Quantum correlations, 617
Quantum coulomb solution
BRST charge, 383
BRST exact, 385, 386
BRST quantization, 385
electromagnetic field, 382
Feynman gauge, 384
gauge fixed Hamiltonian, 383–385
Heisenberg picture, 386
infrared regularization, 386
modified vacuum state, 382
polarization vectors, 383
Quantum critical point (QCP), 329, 331,
333–335, 340
Quantum electrodynamics (QED), 569
Quantum electrodynamics in three dimensions
(QED 3 ), 328–333, 335, 338–340,
344
Quantum entanglement
area-law, 347
distribution, 347, 348
geometry, 348
Quantum Finite W -Algebras
lax type operators, 191
twisted Yangians, 192
Quantum invariants, 295–303
Quantum 6j -symbols, 278, 283
Quantum knot invariants, 277
Quantum Monte Carlo (QMC) simulations,
338
critical exponents, 343–344
principle, 343
Quantum phase transitions, 337
Quantum processes
algorithm, 645
Bell inequalities, 616
causal hypotheses, 621
causal inference methods, 616
causal relations, 617, 620
cause-effect relations, 615, 618–620
commutant algebra, 646
equivalent representations, 647
Hermitian Matrix, 646
interrogations, 625
measurements, 617
notation, 617–618
post-processing real representations, 647
probabilistic theories, 616
scenario, 623–625
variables, 616
Quantum terms, 451
Quantum theory, 413
Quantum volume conjecture, 278
Quantum vortices, 445
Quartet mechanism, 372
Quasi-Maximally superintegrable (QMS)
Bertrand theorem, 141
Hamiltonian systems, 142
metrics/scalar curvature, 142, 143
quantum model, 144–147
radial equation, motion, 143, 144
Quasiparticle properties, 361
Quasi-relativistic evolution equation, 107
Quasi single field inflation (QSFI), 547, 549
R
Racah algebra
definition, 209
differential embedding, 214, 215
higher rank, 210, 211
Rn, 212–213
sln , n-1 variables, 211–212
U(Dn) operators, 212
Racah coefficients, 283
Rainbow state, 348, 351
Rational difference equations, 69
Rational transformations, 22
Recursive solution, 104–107
Reheating, 431
Renormalization-group approach, 344
RepLAB features, 648
CHSH expression, 643
decompose, 644
MATLAB, 644
unique features, 644–645
Representation theory
algebraic results, 135, 136
Bruhat decomposition, 132
Casimir operators, 138
Index
Quad equation, 22–23
algebraic entropy, 28
CAC, 24
discrete Lax pairs, 23–24
Lax pair from CAC, 24–25
singularity structure, 26–27
square lattice, evolution, 28–29
symmetries, 25–26
vertical/horizontal symmetries (see
Symmetries)
Quantum advantages
coherence, 622
random variables, 622
Quantum affine W-algebra, 181
Quantum canonical transformation, 523
Quantum causal models, 616
Quantum computing, 309
Quantum corrections, 448
Quantum correlations, 617
Quantum coulomb solution
BRST charge, 383
BRST exact, 385, 386
BRST quantization, 385
electromagnetic field, 382
Feynman gauge, 384
gauge fixed Hamiltonian, 383–385
Heisenberg picture, 386
infrared regularization, 386
modified vacuum state, 382
polarization vectors, 383
Quantum critical point (QCP), 329, 331,
333–335, 340
Quantum electrodynamics (QED), 569
Quantum electrodynamics in three dimensions
(QED 3 ), 328–333, 335, 338–340,
344
Quantum entanglement
area-law, 347
distribution, 347, 348
geometry, 348
Quantum Finite W -Algebras
lax type operators, 191
twisted Yangians, 192
Quantum invariants, 295–303
Quantum 6j -symbols, 278, 283
Quantum knot invariants, 277
Quantum Monte Carlo (QMC) simulations,
338
critical exponents, 343–344
principle, 343
Quantum phase transitions, 337
Quantum processes
algorithm, 645
Bell inequalities, 616
causal hypotheses, 621
causal inference methods, 616
causal relations, 617, 620
cause-effect relations, 615, 618–620
commutant algebra, 646
equivalent representations, 647
Hermitian Matrix, 646
interrogations, 625
measurements, 617
notation, 617–618
post-processing real representations, 647
probabilistic theories, 616
scenario, 623–625
variables, 616
Quantum terms, 451
Quantum theory, 413
Quantum volume conjecture, 278
Quantum vortices, 445
Quartet mechanism, 372
Quasi-Maximally superintegrable (QMS)
Bertrand theorem, 141
Hamiltonian systems, 142
metrics/scalar curvature, 142, 143
quantum model, 144–147
radial equation, motion, 143, 144
Quasiparticle properties, 361
Quasi-relativistic evolution equation, 107
Quasi single field inflation (QSFI), 547, 549
R
Racah algebra
definition, 209
differential embedding, 214, 215
higher rank, 210, 211
Rn, 212–213
sln , n-1 variables, 211–212
U(Dn) operators, 212
Racah coefficients, 283
Rainbow state, 348, 351
Rational difference equations, 69
Rational transformations, 22
Recursive solution, 104–107
Reheating, 431
Renormalization-group approach, 344
RepLAB features, 648
CHSH expression, 643
decompose, 644
MATLAB, 644
unique features, 644–645
Representation theory
algebraic results, 135, 136
Bruhat decomposition, 132
Casimir operators, 138