Index
229
π j (A), 77
π E E , 109
ψ (±) ∈ H
±
N , 69
ψ E : H N ψ E = Eψ E , 173
dim(E) := max{dim(F) : F ∈ supp
E},
107
dim(F), 107
ρ, 83
ρ G , 84
σ (P(H), C(H))-topology, 22
σ (A, S), 19
σ (A ∗ , A)-topology, 17
σ (A v , (A v ) ∗ )-continuous, 17
σ : G → ∗ - Aut A, g → σ g , 106
σ G , 106
σ ∗
G , 86
σ ξ (ξ ∈ g), 32
τ -KMS state at value β = ∞, 152
τ -KMS state at value β ∈ R, 152
τ -ground state, 152
τ Q , 129, 154, 155
τ Q ⊂ ∗ - Aut C, 135
τ π , 135
τ K (K ∈ ), 129
τ c , 129
τ
Q
t : A N → s G A ∗∗ , 124
τ t c := e it H c e −it H , 181
θ is a two form on g, 106
θ(t)-function, 181
ε(p), 204
{m ◦ }, 88
a θ , 107
b ∗ (ϕ), b(ϕ), 204
b j ∈ A, 197
e ∗ , 111
e ∗ ω = ˜
ω, 104
e ∗ ω ∈ S ∗ (A ∗∗ ), 106
f (t), 181
f → f + , 181
f ξ : F → f ξ (F) := F(ξ ), 115
f ξ (ξ ∈ g), 14
f ξ ∈ C ∞ (g ∗ , R), 115
f m (t), 181
g(ψ 1 , ψ 2 )(t , t ), 190
g(t), 181
g · x := U(g)x, 35
g j := a j a ∗
j a ∗
j+1 a j+1 , 172
g Q : R × g ∗ → G,
(t; F) → g Q (t, F),
116
h ∈ L(h) := L(L
∈ (R
, d
§)), 204
h ± (t), 181
m ∈ Z := ES(Z), 104
m ◦ , 99
m ◦ is an isolated point, 104
n G =: 2k G , 108
pg ∗ , 87
p ω ∈ M
G , 103
ˆ
p ∗
ω , 123
p E := E(g ∗ ), 107
p G , 97
p G ω(x), 99
p ◦
G := p E for E ∈ [E] ◦
G , 110
p J , 87
p M , 99
p M : S(A) → S ∗ (M G ), 111
p M ω, 99
p M ω := μ ω
g , 102
ˆ
p ω , 123
q E, 108
r M , 103
r M ω m , 103
r A , 104
r n E, 109
r M , 111
r M : S(A ∗∗ ) → S(M), 106
s ∗ -topology on A, 139
s ∗ ( p G A ∗∗ , p G A ∗ )-topology, 135
s ∗ (s G A ∗∗ , s G A ∗ )-topology, 123
s G ∈ Z, 83, 131
s μ ∈ Z, 98
s π E
g , 131
s π ∈ Z, 131
sp(X ξ N ), 132
sp(π(X ξ N )), 132
v x := T x x (v) ∈ [x] ⊥ , 24
w(ψ), 186
X N
j , 114
z ∈ O x = O z , 36
A G (⊂ H), 35
C := A ⊗ B, 180
D G ⊂ H, 35
ES(N G ), 94
E(g), 43
E g (⊂ S d
g ), 89
F (h) ≡ ˆ
h, 181
F −1 , 182
H is the Hilbert space, 3
H
, 78
H 1 ⊂ H, 204
H A , 181
H W ⊂ H B , 195
H , 77, 79
H
, 80
H {∅} := {λλ 0 : λ ∈ C}, 172
H vac , 171
K ≡ (H A ⊕ H {∅} ) ⊗ H B , 186