230
Index
K β , 152
L(H), 78
L(H ), 78
M, 85
M G := g ∗ ∪ {m ◦ }, 101
M := ES(M
G ), 104
M ∗ , 87
N , 94, 142
N , 100
S(C), 180
S
g = p G S(A ), 99
U n , 174
Z, 106
d(h), 204
rank(λ F ), 109
ϕ Q , 154
ϕ G , 115
ϕ x := W x ϕ (x ∈ R 2n ), 51
‘Transition probabilities’, 27
(G-)macroscopic algebra, 84
(G-)pure orbits, 89
(Strongly) equivalent, 78
*-automorphisms, 9
0 := S
0 ⊗ F
0 , 204
β N (ψ), 204
β n , 204
z-classical, 45
z-classical operator, 44
conv(B), 131
2-cohomology group H 2 (g, R), 15
A
Absolute value, 22
Adjoint representation, 32
Algebra E(g) λ , 54
Algebra of G-definiteness, 84
Algebra of G-macroscopic observables, 84
Algebra of observables, 16
Algebra of quasilocal observables, 95
Analytic domain A G , 32
Analytic vectors of U (G), 35
Antiunitary transformations, 27
Any concept, 170
Asymptotic abelianess, 151
Atlas on P(H), 23
B
Bardeen-Cooper-Schrieffer model, 160
BCS theory, 160
Berezin bracket, 118
Bessel function J n (z), 174
Bogoliubov-Haag Hamiltonian, 155
Borel ∗ -algebra, 107
Borel*- (resp. the W*-) algebra, 111
Bose particles, 68
Bosons, 68
C
Canonical
Anticommutation
Relation
(CAR), 197
Canonical Commutation Relations (CCR),
50
Canonical
cyclic
representation
{π ω , H ω , ϕ ω }, 88
Center Z(A), 4
Central cover, 84, 153
Central decomposition, 153
Central extension, 10, 11, 49, 66
Central extension G m , 15
Central extension of G by R, 62
Central support, 84
Change of interpretation of the generators,
53
Change of the value of , 53
Characteristic bundle, 70
Charts (N x ; x ; [x] ⊥ ), 32
Choquet simplexes, 18
Classical field theory, 11
Classical interpretation, 29
Classical Mechanics (CM), 1
Classical observable corresponding to the
quantal observable, 43
Classical phase space, 41
Classical Poisson brackets on R 2n , 52
Classical spin, 64, 66
Classical spin from SO(3), 62
Classical states, 113, 119
Classical statistical physics, 211
Classical subsystems, 4
Clopen set, 86, 87
Coadjoint representation Ad ∗ (G), 38
Cocycle g Q , 117
Cocycle identities, 116
Cofinal subset, 110
Collapse, 212
Collapse of its wave packet, 208
Commutator in g, 14
Commutator of vector fields, 14
Complementable, 36
Complete, 115
Complete Tensor Product Space (CTPS), 76,
77
Complete vector field, 3
Index
K β , 152
L(H), 78
L(H ), 78
M, 85
M G := g ∗ ∪ {m ◦ }, 101
M := ES(M
G ), 104
M ∗ , 87
N , 94, 142
N , 100
S(C), 180
S
g = p G S(A ), 99
U n , 174
Z, 106
d(h), 204
rank(λ F ), 109
ϕ Q , 154
ϕ G , 115
ϕ x := W x ϕ (x ∈ R 2n ), 51
‘Transition probabilities’, 27
(G-)macroscopic algebra, 84
(G-)pure orbits, 89
(Strongly) equivalent, 78
*-automorphisms, 9
0 := S
0 ⊗ F
0 , 204
β N (ψ), 204
β n , 204
z-classical, 45
z-classical operator, 44
conv(B), 131
2-cohomology group H 2 (g, R), 15
A
Absolute value, 22
Adjoint representation, 32
Algebra E(g) λ , 54
Algebra of G-definiteness, 84
Algebra of G-macroscopic observables, 84
Algebra of observables, 16
Algebra of quasilocal observables, 95
Analytic domain A G , 32
Analytic vectors of U (G), 35
Antiunitary transformations, 27
Any concept, 170
Asymptotic abelianess, 151
Atlas on P(H), 23
B
Bardeen-Cooper-Schrieffer model, 160
BCS theory, 160
Berezin bracket, 118
Bessel function J n (z), 174
Bogoliubov-Haag Hamiltonian, 155
Borel ∗ -algebra, 107
Borel*- (resp. the W*-) algebra, 111
Bose particles, 68
Bosons, 68
C
Canonical
Anticommutation
Relation
(CAR), 197
Canonical Commutation Relations (CCR),
50
Canonical
cyclic
representation
{π ω , H ω , ϕ ω }, 88
Center Z(A), 4
Central cover, 84, 153
Central decomposition, 153
Central extension, 10, 11, 49, 66
Central extension G m , 15
Central extension of G by R, 62
Central support, 84
Change of interpretation of the generators,
53
Change of the value of , 53
Characteristic bundle, 70
Charts (N x ; x ; [x] ⊥ ), 32
Choquet simplexes, 18
Classical field theory, 11
Classical interpretation, 29
Classical Mechanics (CM), 1
Classical observable corresponding to the
quantal observable, 43
Classical phase space, 41
Classical Poisson brackets on R 2n , 52
Classical spin, 64, 66
Classical spin from SO(3), 62
Classical states, 113, 119
Classical statistical physics, 211
Classical subsystems, 4
Clopen set, 86, 87
Coadjoint representation Ad ∗ (G), 38
Cocycle g Q , 117
Cocycle identities, 116
Cofinal subset, 110
Collapse, 212
Collapse of its wave packet, 208
Commutator in g, 14
Commutator of vector fields, 14
Complementable, 36
Complete, 115
Complete Tensor Product Space (CTPS), 76,
77
Complete vector field, 3