232
Index
Inner product, 13
Integrable subbundle, 70
Interaction Hamiltonian, 179
Interpretation, 9
Interpretation of observables, 41
Involution, 16
Irreducible, 7
Irreducibly statistical theory, 211
Irreversible behaviour, 208
Isotropy subgroup, 63
J
Jordan-Wigner transformation, 197
K
Kähler structure, 21, 26
Kirillov-Kostant symplectic form, 39, 116
Kirillov-Kostant symplectic orbit, 41
Kirillov-Kostant symplectic structure, 83
Klaus Hepp, 168
KMS-condition, 151
KMS states, 151, 163
Knowledge as a “model”, 169
L
Leaf of this foliation, 70
Leibniz rule, 19
Lie algebra of G, 14
Lie algebra structure, 13
Lie algebra U (g) of generators, 35
Lie derivative, 13
Lie group, 3, 14
Limit → 0, 53
Linear space T(H), 7
Linear superposition, 210
Local algebras, 95
Local Hamiltonians Q N , 113, 114
Locally Hamiltonian, 13
Locally normal states, 17
Local observables, 95
Local subalgebra of A, 17
Local time evolutions, 113
Lower semicontinuous, 109
M
Macroscopic algebra of G-definiteness, 111
Macroscopically distinguishable, 18
Macroscopically pure, 163
Macroscopically stationary, 163
Macroscopic interference, 212
Macroscopic limit, 4, 105
Macroscopic quantity, 208
Macroscopic quantization, 112
Manifold modeled by, 11
Manifold structure, 23
Maximal G-measures, 110
Mean-field time evolution, 147
Meaning of ‘the truth’, 169
Measures on M G , 102
Measuring apparatus, 167
Metric Q, 24, 25
Microscopic dynamics, 113
Minimal projectors, 86
Minimal wave packet, 56
Model, 168, 169
Multiplier, 10
Multiplier m corresponds to the cocycle, 15
Mutually disjoint, 164
N
N x , 23
Natural foliation, 70
Neighbourhood of x ∈ P(H), 23
Net of local algebras, 16
Nonexistence of a (Liouville) measure on
P(H), 28
Nonideal measurement, 177, 179
Nonlinear (field-) equation, 33
Nontrivial macroscopic limit, 107
Normal, 8
Normal conducting phase, 165
Normal pure states, 86
Normal pure states on M G , 92
Normalized, 8
Norm-asymptotically abelian, 152
O
Observables, 7, 16, 177
Observables in QM, 7
One-parameter group, 9
Orbit O , 3
Orthogonal G−measures, 110
Orthogonal measure, 103
Overcomplete families of vectors, 38
P
Passive state, 152
Pauli σ -matrices, 196
Pictures of the world, 170
Planck constant, 49
Poincaré cycles, 209
Index
Inner product, 13
Integrable subbundle, 70
Interaction Hamiltonian, 179
Interpretation, 9
Interpretation of observables, 41
Involution, 16
Irreducible, 7
Irreducibly statistical theory, 211
Irreversible behaviour, 208
Isotropy subgroup, 63
J
Jordan-Wigner transformation, 197
K
Kähler structure, 21, 26
Kirillov-Kostant symplectic form, 39, 116
Kirillov-Kostant symplectic orbit, 41
Kirillov-Kostant symplectic structure, 83
Klaus Hepp, 168
KMS-condition, 151
KMS states, 151, 163
Knowledge as a “model”, 169
L
Leaf of this foliation, 70
Leibniz rule, 19
Lie algebra of G, 14
Lie algebra structure, 13
Lie algebra U (g) of generators, 35
Lie derivative, 13
Lie group, 3, 14
Limit → 0, 53
Linear space T(H), 7
Linear superposition, 210
Local algebras, 95
Local Hamiltonians Q N , 113, 114
Locally Hamiltonian, 13
Locally normal states, 17
Local observables, 95
Local subalgebra of A, 17
Local time evolutions, 113
Lower semicontinuous, 109
M
Macroscopic algebra of G-definiteness, 111
Macroscopically distinguishable, 18
Macroscopically pure, 163
Macroscopically stationary, 163
Macroscopic interference, 212
Macroscopic limit, 4, 105
Macroscopic quantity, 208
Macroscopic quantization, 112
Manifold modeled by, 11
Manifold structure, 23
Maximal G-measures, 110
Mean-field time evolution, 147
Meaning of ‘the truth’, 169
Measures on M G , 102
Measuring apparatus, 167
Metric Q, 24, 25
Microscopic dynamics, 113
Minimal projectors, 86
Minimal wave packet, 56
Model, 168, 169
Multiplier, 10
Multiplier m corresponds to the cocycle, 15
Mutually disjoint, 164
N
N x , 23
Natural foliation, 70
Neighbourhood of x ∈ P(H), 23
Net of local algebras, 16
Nonexistence of a (Liouville) measure on
P(H), 28
Nonideal measurement, 177, 179
Nonlinear (field-) equation, 33
Nontrivial macroscopic limit, 107
Normal, 8
Normal conducting phase, 165
Normal pure states, 86
Normal pure states on M G , 92
Normalized, 8
Norm-asymptotically abelian, 152
O
Observables, 7, 16, 177
Observables in QM, 7
One-parameter group, 9
Orbit O , 3
Orthogonal G−measures, 110
Orthogonal measure, 103
Overcomplete families of vectors, 38
P
Passive state, 152
Pauli σ -matrices, 196
Pictures of the world, 170
Planck constant, 49
Poincaré cycles, 209