Index
231
Complex structure J on P ( H), 25
Composite system, 208
Contact manifold, 48
Contact structure, 3
Contraction, 130
Convex hull, 131
Convex W ∗ -compact, 153
Convolution, 52
Convolution f ∗ h(t), 181
Core D ⊂ H of a closable operator, 32
Correspondence between classical and quantal observables, 42
Cotangent bundle T ∗ (M), 61
Covariant representations, 20
Covering symplectic space, 62
Cross norm, 129
Cyclic representation, 18
Cyclic vector, 18
D
Density matrices, 7, 208
Derivation δ π , 135
Derivation δ Q , 147
Derivation on A, 19
Difference between QM and CM, 28
Differential geometry, 11
Dimension of E g , the, 111
Dirac measures, 12
Disjoint, 18, 153, 176, 178, 180
Disjointness, 208
Disjoint : ω 1 ⊥ ω 2 , 19
Disjoint representations, 19
Disjoint states, 202
Distance functions, 21, 22, 25
Domain D(A) ⊂ H, 28
E
Embedding of C bs into A ∗∗ , 142
Environment, 203
Environment ≡ the Fermi field, 208
Equivalent cocycle, 15
Euclidean or Poincaré transformations, 19
Exactly homogeneous, 15
Expectation values, 8, 29
Extended phase space, 3
Exterior differential, 31
Extremal decomposition, 153
Extremal KMS states, 163
Extremal (τ Q , β := T −1 )-KMS states, 164
Extremal τ Q -ground state, 165
Extremal τ Q -KMS state, 163
Extreme points of S ∗ , 7
F
Face, 102, 153
Factor-space of H, 21
Factor states, 88, 153
Factor-topology, 21
Fermions, 68
Fermi particles, 68
Final truth, 170
Finitely additive Borel measure, 88
Fourier transform F , 181, 205
Fubini-Study metric, 26
G
Galilean group, 66
Gårding domain D G , 32
Gårding domain of U (G), 35
Gårding domain of U (G n ), 58
Gauge-invariant KMS-states, 164
Generalized G-macroscopic phase space,
101
Generalized z-classical operator, 44
Generator, 9
G-equivariant, 101
Globally Hamiltonian, 3
Globally Hamiltonian vector fields, 41
G-macroscopically pure orbits, 89
G-macroscopically pure states, 101
G-macroscopic state, 101
GNS-algorithm, 18
G-pure states, 89
H
Hamiltonian function, 13, 102
Hamiltonian vector field, 13, 102
Hamiltonian vector field σ Q , 115
Hamiltonian vector field on M, 45
Heisenberg group, 49
Hilbert-Schmidt operator topology, 22
Homogeneous space, 14
Human construction, 170
I
Ideal measurements, 169, 180, 202
Identical particles, 67, 68
Immersed submanifold, 70
Immersion, 70
Imprimitivity system, 112
Incomplete Tensor Product Space (ITPS), 78
Indistinguishable, 68
Inner automorphisms, 11, 19
231
Complex structure J on P ( H), 25
Composite system, 208
Contact manifold, 48
Contact structure, 3
Contraction, 130
Convex hull, 131
Convex W ∗ -compact, 153
Convolution, 52
Convolution f ∗ h(t), 181
Core D ⊂ H of a closable operator, 32
Correspondence between classical and quantal observables, 42
Cotangent bundle T ∗ (M), 61
Covariant representations, 20
Covering symplectic space, 62
Cross norm, 129
Cyclic representation, 18
Cyclic vector, 18
D
Density matrices, 7, 208
Derivation δ π , 135
Derivation δ Q , 147
Derivation on A, 19
Difference between QM and CM, 28
Differential geometry, 11
Dimension of E g , the, 111
Dirac measures, 12
Disjoint, 18, 153, 176, 178, 180
Disjointness, 208
Disjoint : ω 1 ⊥ ω 2 , 19
Disjoint representations, 19
Disjoint states, 202
Distance functions, 21, 22, 25
Domain D(A) ⊂ H, 28
E
Embedding of C bs into A ∗∗ , 142
Environment, 203
Environment ≡ the Fermi field, 208
Equivalent cocycle, 15
Euclidean or Poincaré transformations, 19
Exactly homogeneous, 15
Expectation values, 8, 29
Extended phase space, 3
Exterior differential, 31
Extremal decomposition, 153
Extremal KMS states, 163
Extremal (τ Q , β := T −1 )-KMS states, 164
Extremal τ Q -ground state, 165
Extremal τ Q -KMS state, 163
Extreme points of S ∗ , 7
F
Face, 102, 153
Factor-space of H, 21
Factor states, 88, 153
Factor-topology, 21
Fermions, 68
Fermi particles, 68
Final truth, 170
Finitely additive Borel measure, 88
Fourier transform F , 181, 205
Fubini-Study metric, 26
G
Galilean group, 66
Gårding domain D G , 32
Gårding domain of U (G), 35
Gårding domain of U (G n ), 58
Gauge-invariant KMS-states, 164
Generalized G-macroscopic phase space,
101
Generalized z-classical operator, 44
Generator, 9
G-equivariant, 101
Globally Hamiltonian, 3
Globally Hamiltonian vector fields, 41
G-macroscopically pure orbits, 89
G-macroscopically pure states, 101
G-macroscopic state, 101
GNS-algorithm, 18
G-pure states, 89
H
Hamiltonian function, 13, 102
Hamiltonian vector field, 13, 102
Hamiltonian vector field σ Q , 115
Hamiltonian vector field on M, 45
Heisenberg group, 49
Hilbert-Schmidt operator topology, 22
Homogeneous space, 14
Human construction, 170
I
Ideal measurements, 169, 180, 202
Identical particles, 67, 68
Immersed submanifold, 70
Immersion, 70
Imprimitivity system, 112
Incomplete Tensor Product Space (ITPS), 78
Indistinguishable, 68
Inner automorphisms, 11, 19