Index
Symbols
O , 82
ˆ
y(ϕ) := ϕ(y), 103
(A; σ (G); τ Q ; π(()), 152
(A; σ G ), 106
(C; τ Q ; π(()), 152
(g ∗ , λ; ϕ G ), 107, 111, 115
(τ, β)-KMS state, 152
A , 80
A
, 80
C(supp E g , G), 140
C ∗ -dynamical system, 152
C ∗ -inductive limit, 16
C ∗ -products, 128
C ∗ -property, 16
C ∗ -algebra A, 16
C b := C b (K , C), 140
C b := C b (supp E g , C), 139
C t (r ), 198
D (A), 80
D (A), 80
D (g), 81
E( f ) ∈ Z, 107
E ≤ E ⇔ E = Es E , 109
E #
g (B), 85
E
g , 100, 134
E
g (B), 98
E g , 120
E g (F) (F ∈ g ∗ ), 85
E #
g (F) := ρ G (E g (F)), 85
E ξξ (ξ ∈ g), 84
Es E , 108
F(t), 181
F 0 (t), 181
F ∈ g ∗ , 82
F g , 91, 104
F g : M → ˙
M G , 104
F ω , 154
F j := F(ξ j ) = f ξ j (F), 125
G-macroscopic algebra, 111
G-macroscopic limit, 111
G-macroscopic dimension, 108
G-macroscopic limit of the dimension n G ,
108
G-macroscopic number, 108
G-measure, 107
G(t , t ), 190
G max , 58
H n , 196
H ( j,k) , 171
K := supp E g , 144
K ⊂ g ∗ , 140
K ◦
z := K ◦ := {h ∈ G : U(h)z = z}, 36
k
ψ
0 ⊂ g N (:= the Lie algebra of G N , 69
K z · z = [z], 40
M = M z , 40
M , 83
N x , 23
O N
ϕ := V N (G)ϕ, 75
O ω := σ ∗
G ω, 89
O x := G · x, 35
O ϕ := {P
ϕ
x : x ∈ R 2n }, 51
P D(A) ⊂ P(H), 28
P P
ϕ
+ , 69
P ϕ : x → P
ϕ
x , 51
P
ϕ
x ∈ P(H), 51
P G , 83
P G ∈ Z # , 83
P , 78
P D (A), 80
P w
, 78
P λ
j := X λ
j+n , 54
© Springer Nature Switzerland AG 2020, corrected publication 2020
P. Bóna, Classical Systems in Quantum Mechanics,
https://doi.org/10.1007/978-3-030-45070-0
227