Index
331
M
Manne-Dalgaard (operator set), 242, 249
Matrix representation (of diagrams), 91–93
Møller–Plesset partitioning, 45, 201, 219,
220, 271
N
N-electron excitations, 31, 195, 207, 214,
215, 249, 257, 259, 308
Normal-ordering (of operator products), 62–
64, 284–285
operator, 63
O
Operators
creation operator, 20–21, 27–29, 55, 62,
64, 66, 67, 305
destruction operator, 19–22, 27–29, 31,
38, 55, 62, 64, 66, 67
fermion operator, 20, 28, 32, 49, 61, 62,
64, 69, 126, 182, 284, 305
field operator, 19, 29, 127
Heisenberg operator, 31, 40, 46, 53, 54,
197
one-particle operators, 8–11, 29, 36, 173,
233
permutation operator, 4, 6, 8
physical/unphysical operators, 62, 63,
65, 258, 284–285, 303, 306
in second quantization, 22–24, 30
two-particle operators, 8, 9, 11–14, 29
Order Relations (OR)
canonical order relations (COR), 165,
177–181, 214, 245, 304–311
Orthogonalization
excitation class orthogonalization
(ECO), 161–166, 206, 207
Gram–Schmidt orthogonalization, 162,
178, 179, 183, 245, 253
symmetric orthogonalization, 162, 163,
166, 207
Outer-Valence Green’s Function (OVGF)
method, 132–133, 135
P
Partitioning (of a matrix):
inversion of a partitioned matrix, 273–
274
partitioning of an eigenvalue problem,
274–276
Pauli principle, 4, 7
Permutation
permutation operator, 4, 8
permutation symmetry, 4
Perturbation theory
Brillouin-Wigner (BW) perturbation theory, 270, 277–278
Rayleigh-Schr¨ odinger perturbation theory (RSPT), 45, 55–59, 269–273, 300,
302
time-dependent perturbation theory, 46–
50, 312
Plasmons, 223
Polarizability, 196, 277, 312
Polarization, 230, 231, 252
Polarization propagator, see Propagators
Pole strength, 35, 131, 132
Propagators, see also Green’s functions
electron propagator (one-particle
Green’s function), 31–40, 46, 54, 61,
65, 66, 82, 95, 99, 111, 114–122, 123,
125, 131, 133, 135, 141, 144, 145, 158,
159, 161, 172, 195–198, 201, 210, 248,
314, 316–318, 320
free electron propagator (free oneparticle Green’s function), 40–41, 61,
103, 124, 200
polarization propagator, 31, 135, 195–
204, 208–214, 223, 228, 312–315
R
Random-Phase Approximation (RPA), 135,
198, 218, 223–236, 251–253
RPA diagrams, 210, 223, 224
RPA pseudo-eigenvalue problem, 225–
229, 250
Rank (of an operator), 305–306
Regularity (of PT expansions), 143, 156
Relaxation, 230, 231, 252
S
Satellite (shake-up) states, 130
Scaling, 157, 214
Schr¨ odinger representation, 46
Second quantization, 19–30
Self-Consistent Field (SCF), see HartreeFock (HF)
Self-energy, 111–124
diagrams, 115–119, 139
dynamical self-energy part, 119, 124,
135–140, 297–299
improper self-energy part, 112
331
M
Manne-Dalgaard (operator set), 242, 249
Matrix representation (of diagrams), 91–93
Møller–Plesset partitioning, 45, 201, 219,
220, 271
N
N-electron excitations, 31, 195, 207, 214,
215, 249, 257, 259, 308
Normal-ordering (of operator products), 62–
64, 284–285
operator, 63
O
Operators
creation operator, 20–21, 27–29, 55, 62,
64, 66, 67, 305
destruction operator, 19–22, 27–29, 31,
38, 55, 62, 64, 66, 67
fermion operator, 20, 28, 32, 49, 61, 62,
64, 69, 126, 182, 284, 305
field operator, 19, 29, 127
Heisenberg operator, 31, 40, 46, 53, 54,
197
one-particle operators, 8–11, 29, 36, 173,
233
permutation operator, 4, 6, 8
physical/unphysical operators, 62, 63,
65, 258, 284–285, 303, 306
in second quantization, 22–24, 30
two-particle operators, 8, 9, 11–14, 29
Order Relations (OR)
canonical order relations (COR), 165,
177–181, 214, 245, 304–311
Orthogonalization
excitation class orthogonalization
(ECO), 161–166, 206, 207
Gram–Schmidt orthogonalization, 162,
178, 179, 183, 245, 253
symmetric orthogonalization, 162, 163,
166, 207
Outer-Valence Green’s Function (OVGF)
method, 132–133, 135
P
Partitioning (of a matrix):
inversion of a partitioned matrix, 273–
274
partitioning of an eigenvalue problem,
274–276
Pauli principle, 4, 7
Permutation
permutation operator, 4, 8
permutation symmetry, 4
Perturbation theory
Brillouin-Wigner (BW) perturbation theory, 270, 277–278
Rayleigh-Schr¨ odinger perturbation theory (RSPT), 45, 55–59, 269–273, 300,
302
time-dependent perturbation theory, 46–
50, 312
Plasmons, 223
Polarizability, 196, 277, 312
Polarization, 230, 231, 252
Polarization propagator, see Propagators
Pole strength, 35, 131, 132
Propagators, see also Green’s functions
electron propagator (one-particle
Green’s function), 31–40, 46, 54, 61,
65, 66, 82, 95, 99, 111, 114–122, 123,
125, 131, 133, 135, 141, 144, 145, 158,
159, 161, 172, 195–198, 201, 210, 248,
314, 316–318, 320
free electron propagator (free oneparticle Green’s function), 40–41, 61,
103, 124, 200
polarization propagator, 31, 135, 195–
204, 208–214, 223, 228, 312–315
R
Random-Phase Approximation (RPA), 135,
198, 218, 223–236, 251–253
RPA diagrams, 210, 223, 224
RPA pseudo-eigenvalue problem, 225–
229, 250
Rank (of an operator), 305–306
Regularity (of PT expansions), 143, 156
Relaxation, 230, 231, 252
S
Satellite (shake-up) states, 130
Scaling, 157, 214
Schr¨ odinger representation, 46
Second quantization, 19–30
Self-Consistent Field (SCF), see HartreeFock (HF)
Self-energy, 111–124
diagrams, 115–119, 139
dynamical self-energy part, 119, 124,
135–140, 297–299
improper self-energy part, 112