330
Index
Dyson-ADC equations, 140–145
Dyson expansion method (DEM), 295–
299
Dyson orbital, 126–127
Dyson secular matrix, 124–126, 147, 157
E
Energy representation (of propagators, diagrams), 33, 34, 37, 39, 40, 95, 98–
100, 115–117, 195–197, 203, 224,
314
Electron attachment, 31, 32, 125, 257
energy (electron affinity), 33, 34, 125,
132
Electron density
density function, 123
one-particle density matrix, 36, 37, 122,
123, 158, 172, 174
Electron propagator, see Propagator
Equations-of-motion (EOM)
for many-body Green’s functions, 38, 40,
41
for ionization/electron attachment, 241–
245
for N-electron excitations, 249–253
EOM-CC, see Coupled-cluster methods
F
Factorization theorem, 183–184, 265–266
Fermion operator, see Operators
Fermion line
closed loop, 77–79, 85, 106, 123, 202,
203
continuous, 79, 201–203
free (or G 0 -line), 66, 67, 79–80, 88, 107,
201, 202, 289
Feynman diagrams, see Diagrams
Field operator, see Operators
Fock space, 19, 20, 246, 247
G
Gell-Mann and Low theorem, 46, 50–53,
199, 279–282, 293
Goldstone diagrams, see Diagrams
Green’s functions, see also Propagators
free one-particle (free electron propagator), 40, 64, 66, 77, 81, 87, 96, 201, 290
one-particle (electron propagator), 31–
36, 41, 197
two-particle, 38, 197
Ground-state energy, 37–39, 52, 55–56,
129–130, 143, 159, 165, 170, 190,
207, 229, 258, 272, 277, 278
Ground-state expectation value, 36–37, 53–
54, 65, 71, 158, 168, 186, 199, 200,
216, 217, 316
GW approximation, 135
H
Hartree-Fock (HF)
approximation, 24, 45
diagrams in HF representation, 81–82
Heisenberg operator, see operators
Heisenberg representation, 197
Hubbard hamiltonian, 24
Hubbard diagrams, see Diagrams
I
Infinite partial summation (of diagrams),
111, 135, 143, 156, 223
Interaction symbols:
cross, 80, 81
dot, 83–87, 115, 144, 202
wiggly interaction line, 66, 77, 79, 80,
85, 123, 201, 202, 289
Interaction picture, 46–48, 50, 51, 53, 55, 62,
312, 313
Intermediate state representation (ISR)
for N±1 electrons, 161–170
for N electrons, 205–207, 214
ISR of operators, 170–174, 215–216
Ionization, 31
energy, 34, 129–131, 174, 190, 191
K
Killer Condition (KC), 242–243, 249–252
Koopmans’ theorem, 129
L
Length form, see Transition moments
Linear response theory, 312–315
linear response function, 313
particle-hole (p-h) response function,
197, 198
Linked-cluster theorem, 55, 59, 61, 68, 70–
72, 145
generalized linked-cluster theorem, 257,
264, 302–304
Index
Dyson-ADC equations, 140–145
Dyson expansion method (DEM), 295–
299
Dyson orbital, 126–127
Dyson secular matrix, 124–126, 147, 157
E
Energy representation (of propagators, diagrams), 33, 34, 37, 39, 40, 95, 98–
100, 115–117, 195–197, 203, 224,
314
Electron attachment, 31, 32, 125, 257
energy (electron affinity), 33, 34, 125,
132
Electron density
density function, 123
one-particle density matrix, 36, 37, 122,
123, 158, 172, 174
Electron propagator, see Propagator
Equations-of-motion (EOM)
for many-body Green’s functions, 38, 40,
41
for ionization/electron attachment, 241–
245
for N-electron excitations, 249–253
EOM-CC, see Coupled-cluster methods
F
Factorization theorem, 183–184, 265–266
Fermion operator, see Operators
Fermion line
closed loop, 77–79, 85, 106, 123, 202,
203
continuous, 79, 201–203
free (or G 0 -line), 66, 67, 79–80, 88, 107,
201, 202, 289
Feynman diagrams, see Diagrams
Field operator, see Operators
Fock space, 19, 20, 246, 247
G
Gell-Mann and Low theorem, 46, 50–53,
199, 279–282, 293
Goldstone diagrams, see Diagrams
Green’s functions, see also Propagators
free one-particle (free electron propagator), 40, 64, 66, 77, 81, 87, 96, 201, 290
one-particle (electron propagator), 31–
36, 41, 197
two-particle, 38, 197
Ground-state energy, 37–39, 52, 55–56,
129–130, 143, 159, 165, 170, 190,
207, 229, 258, 272, 277, 278
Ground-state expectation value, 36–37, 53–
54, 65, 71, 158, 168, 186, 199, 200,
216, 217, 316
GW approximation, 135
H
Hartree-Fock (HF)
approximation, 24, 45
diagrams in HF representation, 81–82
Heisenberg operator, see operators
Heisenberg representation, 197
Hubbard hamiltonian, 24
Hubbard diagrams, see Diagrams
I
Infinite partial summation (of diagrams),
111, 135, 143, 156, 223
Interaction symbols:
cross, 80, 81
dot, 83–87, 115, 144, 202
wiggly interaction line, 66, 77, 79, 80,
85, 123, 201, 202, 289
Interaction picture, 46–48, 50, 51, 53, 55, 62,
312, 313
Intermediate state representation (ISR)
for N±1 electrons, 161–170
for N electrons, 205–207, 214
ISR of operators, 170–174, 215–216
Ionization, 31
energy, 34, 129–131, 174, 190, 191
K
Killer Condition (KC), 242–243, 249–252
Koopmans’ theorem, 129
L
Length form, see Transition moments
Linear response theory, 312–315
linear response function, 313
particle-hole (p-h) response function,
197, 198
Linked-cluster theorem, 55, 59, 61, 68, 70–
72, 145
generalized linked-cluster theorem, 257,
264, 302–304