Index
233
Poincaré group, 66
Poisson action, 15
Poisson algebra structure, 12
Poisson bracket, 13, 102
Poisson manifold, 101, 115
Poisson structure, 102, 106
Polarization identity, 141, 191
Polynomials in selfadjoint generators, 43
Pontius Pilate, 169
Positive Operator Valued Measure (POVM),
169, 177, 180
Predual of A, 17
Probability distribution, 29
Probability of the detection, 186
Probability w(ψ) as a diagonal matrix element, 180
Process R, 203
Product-vector in H , 77
Projection-valued measure, 177
Projective Hilbert space, 21
Projective Hilbert space P(H), 3, 8
Projective representation, 10
Projective system, 109
Projector Valued Measure (PVM), 9, 169,
177
Property (SA), 114
Pseudosupported, 153
Pull-back, 26, 41 153
Purely n-dimensional, 109
Purely nontrivial, 109
Pure states, 8, 12, 17,
Q
Quantum Domino (QD), 168, 170
Quantum mean-field evolutions, 115
Quantum mean-field theories, 113
Quantum measurement, 167
Quantum Mechanics (QM), 1
Quasilocal algebras, 19
Quasilocal structure, 95
Quasilocal structure of A, 16
Quasilocal with respect to the action, 17
Quasi spin formulation, 160
R
Reality, 169
Reduction postulate, 212
Representation ρ, 83
Resolvent of the operator H , 205
Restriction mapping, 106
S
Scalar product, 21
Schrödinger equation, 33
Schwarz inequality, 96
Selfadjoint operator, 28
Selfconsistently, 5
Selfintersections, 70
Seminorms, 123
Set of states S ∗ , 7
Short range correlations, 154, 155
Simplex, 8, 12, 153
SNAG-theorem, 99
Sommerfeld integral representation, 174
Space reflection, 172
Spectral measure, 9
Spectral measure of A, 28
Spectrum of H , 205
Spectrum space of M G , 85
Spontaneous symmetry breaking, 164
Spreading of the wave packet, 62
State on M G , 101
States, 7, 12, 17
Stationary points F ∈ su(2) ∗ , 161
Statistical ensembles, 211
Stone- ˇ
Cech compactification, 92
Strictly Hamiltonian, 42
Strongly inequivalent, 78
Strongly nondegenerate, 26
Subimmersion, 70
Submersion, 70
Superconducting phase, 165
Support projector, 111
Symmetries, 7, 12, 19
Symplectic, 26
Symplectic form, 11
Symplectic form on P(H), 26
Symplectic homogeneous spaces, 38
Symplectic isometries, 29
Symplectic isometry of P(H), 29
Symplectic manifold, 11, 12
Symplectic structure, 3
Symplectic transformations, 27
Symplectomorphism, 12
T
Takesaki’s theorem, 156
Tangent space of P(H) at x, 24
Temperature, 152
Tensor field λ, 102
Theorem by Wigner, 27
Theories of quantum measurements, 212
Thermodynamic equilibrium, 151
233
Poincaré group, 66
Poisson action, 15
Poisson algebra structure, 12
Poisson bracket, 13, 102
Poisson manifold, 101, 115
Poisson structure, 102, 106
Polarization identity, 141, 191
Polynomials in selfadjoint generators, 43
Pontius Pilate, 169
Positive Operator Valued Measure (POVM),
169, 177, 180
Predual of A, 17
Probability distribution, 29
Probability of the detection, 186
Probability w(ψ) as a diagonal matrix element, 180
Process R, 203
Product-vector in H , 77
Projection-valued measure, 177
Projective Hilbert space, 21
Projective Hilbert space P(H), 3, 8
Projective representation, 10
Projective system, 109
Projector Valued Measure (PVM), 9, 169,
177
Property (SA), 114
Pseudosupported, 153
Pull-back, 26, 41 153
Purely n-dimensional, 109
Purely nontrivial, 109
Pure states, 8, 12, 17,
Q
Quantum Domino (QD), 168, 170
Quantum mean-field evolutions, 115
Quantum mean-field theories, 113
Quantum measurement, 167
Quantum Mechanics (QM), 1
Quasilocal algebras, 19
Quasilocal structure, 95
Quasilocal structure of A, 16
Quasilocal with respect to the action, 17
Quasi spin formulation, 160
R
Reality, 169
Reduction postulate, 212
Representation ρ, 83
Resolvent of the operator H , 205
Restriction mapping, 106
S
Scalar product, 21
Schrödinger equation, 33
Schwarz inequality, 96
Selfadjoint operator, 28
Selfconsistently, 5
Selfintersections, 70
Seminorms, 123
Set of states S ∗ , 7
Short range correlations, 154, 155
Simplex, 8, 12, 153
SNAG-theorem, 99
Sommerfeld integral representation, 174
Space reflection, 172
Spectral measure, 9
Spectral measure of A, 28
Spectrum of H , 205
Spectrum space of M G , 85
Spontaneous symmetry breaking, 164
Spreading of the wave packet, 62
State on M G , 101
States, 7, 12, 17
Stationary points F ∈ su(2) ∗ , 161
Statistical ensembles, 211
Stone- ˇ
Cech compactification, 92
Strictly Hamiltonian, 42
Strongly inequivalent, 78
Strongly nondegenerate, 26
Subimmersion, 70
Submersion, 70
Superconducting phase, 165
Support projector, 111
Symmetries, 7, 12, 19
Symplectic, 26
Symplectic form, 11
Symplectic form on P(H), 26
Symplectic homogeneous spaces, 38
Symplectic isometries, 29
Symplectic isometry of P(H), 29
Symplectic manifold, 11, 12
Symplectic structure, 3
Symplectic transformations, 27
Symplectomorphism, 12
T
Takesaki’s theorem, 156
Tangent space of P(H) at x, 24
Temperature, 152
Tensor field λ, 102
Theorem by Wigner, 27
Theories of quantum measurements, 212
Thermodynamic equilibrium, 151