228
Index
PD G ⊂ P(H), 32
Q ω , 153
Q λ
j := X λ
j , 54
Q k (ξ 1 , ξ 2 , . . . , ξ n ), 114
R H (ξ ) ≡ (H − ξ I ) −1 , 205
S g ⊂ S(A ), 84
T x P(H), 24
U t := exp(−it H), 181
V N (G), 72
V N (g), 72
V ϕ , 179
W ≡ W γ , 180
W ∗ -algebra, 17
W ∗ −representation, 83
W λ , 54
W 2
γ = W γ , 195
X N
ξ := X ξ (ξ ∈ g), 75
X λ
j := U λ X j (λ)U
−1
λ , 54
X ξξ (ξ ∈ g), 84
Z m
ϕ+ , 70
[E ] ≺ [E], 110
[E] ◦
G , 110
[E] k
G , 110
[E] G , 110
[ω] := F −1 (F ω ), 83
[x] are analytic submanifolds of O z , 40
N , 75
◦ , 39
0 , 171, 179, 181
F
0 , 204
S
0 ∈ H S , 204
χ
0 , 181
X , 172
∅ := 0 , 172
, 16
-macroscopic algebra of G-definiteness,
97
G-macroscopic algebra, 98
β := T −1 := (kT ) −1 , 152
β
Q
Fω ∈ g, 154
β ◦ : F → β ◦
F ∈ g, 116
β
Q
F , 116, 117
F, 82
P
(λ)
x , 54
U (G), 35, 59
λ, 106
λ F (d f, dg), 115
c( pg ∗ ), 87
f ∈ C bs , 140
u : m := gK ◦ → U(g)z, 36
u ◦ : O z = u(G/K ◦ ) → P(H), 39
δ ξ j : A → A, 147
κ N , 122
λ
−1
0 =: (λ 0 ) −1 , 128
H , 76
˙
g ∗ := g ∗ ∪ {∞}, 104
˙
M G := ˙
g ∗ ∪ {m ◦ }, 104
ˆ
μ ω , 103
ˆ
h = F (h), 182
ˆ
x ∈ C(M), 86
ˆ
ϕ E g , 124
˜
ω ∈ S ∗ ((A ) ∗∗ ), 103
p → ε(p), 204
C, 120
F, 204
A ⊗ N c , 128
A N ⊗ N c , 128
A , 78
B(E), 107
B N , 123
B # := (A ) , 83
B # , 79
B N
0 , 120
C G
bs , 140
C J
bs := C bs (supp E g , A J ), 140
C N , 120
C N
π , 134
C G J
bs , 140
C π , 134
C N
π := A N ⊗ N c
π , 134
C bs := C bs (supp E g , A), 139
M G , 84
M
G , 97
M s , 107
N(E), 107
N c , 120, 124
N c
π , 134
N G , 84
N
G , 97
Z, 102, 111
Z # , 79
g max , 58
k ◦
x , 36
c(K ), 87
μ ω
g , 88, 111
ω(E A (B)), 8
ω , 79, 82
ω n
T , 165
ω s
T (T < T c ), 165
ω A&B
0
, 180
ω ◦ (x), 99
ω μ , 98
τ
Q
t , 137
τ π
t , 137
π ω (A), 154
Index
PD G ⊂ P(H), 32
Q ω , 153
Q λ
j := X λ
j , 54
Q k (ξ 1 , ξ 2 , . . . , ξ n ), 114
R H (ξ ) ≡ (H − ξ I ) −1 , 205
S g ⊂ S(A ), 84
T x P(H), 24
U t := exp(−it H), 181
V N (G), 72
V N (g), 72
V ϕ , 179
W ≡ W γ , 180
W ∗ -algebra, 17
W ∗ −representation, 83
W λ , 54
W 2
γ = W γ , 195
X N
ξ := X ξ (ξ ∈ g), 75
X λ
j := U λ X j (λ)U
−1
λ , 54
X ξξ (ξ ∈ g), 84
Z m
ϕ+ , 70
[E ] ≺ [E], 110
[E] ◦
G , 110
[E] k
G , 110
[E] G , 110
[ω] := F −1 (F ω ), 83
[x] are analytic submanifolds of O z , 40
N , 75
◦ , 39
0 , 171, 179, 181
F
0 , 204
S
0 ∈ H S , 204
χ
0 , 181
X , 172
∅ := 0 , 172
, 16
-macroscopic algebra of G-definiteness,
97
G-macroscopic algebra, 98
β := T −1 := (kT ) −1 , 152
β
Q
Fω ∈ g, 154
β ◦ : F → β ◦
F ∈ g, 116
β
Q
F , 116, 117
F, 82
P
(λ)
x , 54
U (G), 35, 59
λ, 106
λ F (d f, dg), 115
c( pg ∗ ), 87
f ∈ C bs , 140
u : m := gK ◦ → U(g)z, 36
u ◦ : O z = u(G/K ◦ ) → P(H), 39
δ ξ j : A → A, 147
κ N , 122
λ
−1
0 =: (λ 0 ) −1 , 128
H , 76
˙
g ∗ := g ∗ ∪ {∞}, 104
˙
M G := ˙
g ∗ ∪ {m ◦ }, 104
ˆ
μ ω , 103
ˆ
h = F (h), 182
ˆ
x ∈ C(M), 86
ˆ
ϕ E g , 124
˜
ω ∈ S ∗ ((A ) ∗∗ ), 103
p → ε(p), 204
C, 120
F, 204
A ⊗ N c , 128
A N ⊗ N c , 128
A , 78
B(E), 107
B N , 123
B # := (A ) , 83
B # , 79
B N
0 , 120
C G
bs , 140
C J
bs := C bs (supp E g , A J ), 140
C N , 120
C N
π , 134
C G J
bs , 140
C π , 134
C N
π := A N ⊗ N c
π , 134
C bs := C bs (supp E g , A), 139
M G , 84
M
G , 97
M s , 107
N(E), 107
N c , 120, 124
N c
π , 134
N G , 84
N
G , 97
Z, 102, 111
Z # , 79
g max , 58
k ◦
x , 36
c(K ), 87
μ ω
g , 88, 111
ω(E A (B)), 8
ω , 79, 82
ω n
T , 165
ω s
T (T < T c ), 165
ω A&B
0
, 180
ω ◦ (x), 99
ω μ , 98
τ
Q
t , 137
τ π
t , 137
π ω (A), 154