Beltrametti E.G., Cassinelli G. — The Logic of Quantum Mechanics (Encyclopedia of Mathematics and Its Applications - Vol 15) :: Электронная библиотека попечительского совета мехмата МГУ

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Beltrametti E.G., Cassinelli G. — The Logic of Quantum Mechanics (Encyclopedia of Mathematics and Its Applications - Vol 15)

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Название: The Logic of Quantum Mechanics (Encyclopedia of Mathematics and Its Applications - Vol 15)

Авторы: Beltrametti E.G., Cassinelli G.

Аннотация:

This volume deals with the foundations as well as the fascinating logic of quantum mechanics. The thorough presentation will guide the reader to a unified view of a theory that together with relativity is regarded as the greatest achievement in physics during this century.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1 edition

Год издания: 1981

Количество страниц: 305

Добавлена в каталог: 12.04.2010

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Предметный указатель

$\mathcal{P}(\mathcal{K})$       105—108
Atom of a lattice      98
Baer*-semigroups      178
Baer*-semigroups and orthomodular lattices      177—179
Baer*-semigroups, closed projections of      178
Bell’s inequality      275
Boolean algebra      97
Boolean algebra, partied      267
Boolean algebra, sub algebra of poset      126
Borel sets      4
Center of lattice      128
Certainly-yes domain      142—143
Chain in a lattice      195
Chain in a lattice, f-closed subspaces      233
Closure relation      120 193 201
Closure relation, orthoclosure      202 212
Closure spaces      193
Closure spaces, closed subspaces of      193
Coherent subspaces      48—49
Commutativity in poset      125—128
Commuting self-adjoint operators      19
Complementarity      26 162—164
Composition conditions      258
Composition of physical systems      61—74 256—264
Conditional connective      222
Conditional connective, classical      222
Conditional connective, Mittelstaedt’s.      224
Conditional connective, quantum      222—225
Conditioned probability with respect to Boolean algebra      285—287
Conditioned probability with respect to event      279—283
Conjunction      219—220
Continuous geometry      110
Convex set of states      6 209
Convex set of states, normed functioned on.      209
Convex set of states, polytope      211
Convex set of states, simplex      213
Convex set of states, strong polytope      213
Coordinatization, Hilbert-space      235—237
Coordinatization, vector-space      230—234
Coproduct of lattices      259
Correlation between subsystems      67— 72 81
Correlation between subsystems, coefficient of      68 273
Covering property      98 123 133 230
Cyclic vector      294
de Morgan’s laws      96 221
Density operators      4
Direct product of lattices      131
Direct sum of lattices      131
Disjoint elements      97
Disjunction      220
Distributive triple      97
Dynamical group      53
Dynamical invariance      244
Dynamics      52—58 249—255
Dynamics of subsystems      72—73
Dynamics, Heisenberg picture      56—57 254
Dynamics, Markovian      54 250
Dynamics, reversible      54 251
Dynamics, Schroedinger equation      55—56
Dynamics, Schroedinger picture      53
Dynamics, stationary      54 250
Einstein, Podolsky, Rosen paradox      69— 72
Entropy of a state      287
Euclidean invariance      41—43
Evolution operator      53
Exclusion principle      65
Faces of convex set      210
Faces of convex set, detectable      211
Faces of convex set, orthoclosed      212
Faces of convex set, stable      213
FLATS      195—197
Free particle      37—41
Free particle, $G_{12}$       101
Gleason’s theorem      115
Greechie’s examples      102
Hamiltonian of free particle      39 247
Hamiltonian operator      55—56 252—254
Heisenberg inequalities      24—26
Hermitian form      233
Hidden-variable theories      171 265
Hidden-variable theories, Bell’s inequality      275
Hidden-variable theories, Bell’s model of      268—270
Hidden-variable theories, contextual      172—174 175—176 271-276
Hidden-variable theories, Kochen and Specker model of      270—271
Hidden-variable theories, local      271—276
Hidden-variable theories, noncontextual      172—175 265— 271
Identical systems      63—65
Imprimitivity system      244
Induced representations      244
Information of state      287
Involution of field      233
Involutive ring      102
Involutive ring, projections of      103
Involutive semigroup      178
Involutive semigroup, projections of      178
Irreducibility      128 134
Isomorphism of orthomodular lattices      130
Join      96
Joint distributions      23 158
Lattices      97
Lattices, A. C.      95
Lattices, amalgamation      102
Lattices, atomic      98
Lattices, atomistic      98
Lattices, complete      97
Lattices, distributive      97
Lattices, implicative      224
Lattices, irreducible      128
Lattices, modular      98
Lattices, orthomodular      97
Lattices, separable      97
Logic of physical system      149 152
Measurement      79 181
Measurement ideal and of first kind      79 180—187
Measurement process      77—86
Measuring instrument      77—86
Meet      96
Mixtures      7 139
Mixtures, decomposition into pure states      7—12
Mixtures, ignorance interpretation of      11—12
Mixtures, nonunique decomposability      9—12 34—37
Modular geometric lattices      232
Modularity      98 107
Modus ponendo ponens      223
Momentum of free particle      38
Morphism of orthomodular lattices      130
Negation      220—221
Nonseparability      71

Observables      153
Observables, associated with $\mathcal{P}(\mathcal{K})$       155
Observables, bounded      153
Observables, compatible      155
Observables, complementarity      162—164
Observables, complete set of compatible      157
Observables, function of      156—157
Observables, joint distribution of compatible      158
Observables, mean value      154
Observables, spectrum      153 158
Observables, sum of      159—161
Observables, variable      154
Operators commuting self-adjoint      19
Operators commuting self-adjoint, complete set of commuting self-adjoint      21
Operators commuting self-adjoint, density      4
Operators commuting self-adjoint, positive      291
Operators commuting self-adjoint, spectral representation      293
Operators commuting self-adjoint, spectrum      14
Operators commuting self-adjoint, trace-class      291—292
Order relation      96
Orthocomplement      96
Orthocomplementation      96 144
Orthocomplementation, relative      130
Orthomodularity      97 229—230
Paradoxes E. P. R.      69—72
Paradoxes E. P. R., Schroedinger cat      84—86
Pauli matrices      31
Physical quantities compatible      19
Physical quantities compatible, as proposition-valued measures      150
Physical quantities compatible, complementary      26
Physical quantities compatible, complete set of compatible      21
Physical quantities compatible, function of compatible      19
Physical quantities compatible, joint probability distributions      23
Physical quantities compatible, mean value      16
Physical quantities compatible, probability distribution      4—5
Physical quantities compatible, probability distribution in a pure state      8
Physical quantities compatible, variance      17
Polytope      211
Polytope, strong      213
POSET      96
Poset, orthocomplete      97
Poset, orthomodular      97
Position of free particle      38
Probability measures      111
Probability measures and covering property      123—124
Probability measures, convex combination of      112
Probability measures, dispersion-free      155
Probability measures, on       115 117 118 121 122
Probability measures, on $G_{12}$       114 116 118 121 122
Probability measures, ordering set of      116
Probability measures, pure      112 122—123
Probability measures, separating set of      116
Probability measures, strongly ordering set of      116
Probability measures, sufficient set of      116
Probability measures, superposition of      120
Probability measures, support of      117
Probability space      172 277
Probability space, generalized      278
Projection postulate von Neumann’s      79
Projection postulate von Neumann’s, Lueders’s      79 182 282—283
Projection-valued measures      294
Projection-valued measures, spectral      4
Projective geometry      232
Projective lattice      232
Proposition-valued measures      150
Propositions      140—142 146—149
Propositions, active picture of      187—188
Propositions, compatible      155—156
Propositions, complementary      162—164
Propositions, lattice of      152—153
Propositions, ordering      142—144
Propositions, orthocomplements      144—146
Propositions, orthogonal      148
Propositions, passive picture of      187—188
Quantum logic      217—225
Quantum superpositions      164—167
Quantum superpositions, exchange property of      167
Random variables      155 277—278
Rank      194—196
Recognition maps      257
Residuated mappings      179
Sasaki projections      99 179
Sasaki projections, properties of      180—181
Schroedinger equation      55—56
Segment of lattice      130
Spectral theorem      293 295
Spectrum continuous      15 158
Spectrum continuous of observables      153
Spectrum continuous of self-adjoint operators      14
Spectrum continuous, point      14 158
Spectrum continuous, simple      294
Spin      30—31
Spin, spin- $\frac{1}{2}$ system      31—34
Spin-statistics connection      65
States of compound systems      65—67
States of subsystems      65—67 (see also “Probability measures”)
States, dispersion-free      155 (see also “Probability measures”)
States, exceptional      268—271 (see also “Probability measures”)
States, mixture      7 (see also “Probability measures”)
States, nonpure      7 139
States, pure      7 140
States, superposition of      8 120 164—167 191—193
States, vector      8 (see also “Probability measures”)
Stone’s theorem      55 245 253
Superposition principle      165
Superselection operators      47
Superselection rules      45—51 167 238—239
Superselection rules and compound systems      73
Superselection rules, continuous      48
Superselection rules, discrete      48
Support      117 299
Tensor product      61 263—264
Tensor product, antisymmetrical      64
Tensor product, symmetrical      64
Trace-class operators      291—292
Transition probability      12 200
Transition-probability spaces      200
Transition-probability spaces, basis of      202
Transition-probability spaces, orthoclosed subsets of      202
Transition-probability spaces, subspaces of      201
Two-slit experiment      283—285
Von Neumann algebras      21 109—110
von Neumann algebras, entropy      287
von Neumann algebras, lattices      110
von Neumann algebras, projection postulate      79
Weights      6 112
Wigner’s theorem      253
Yes-no experiments      137—138 208—210

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