Bibliography on quantum logics and related structures
International Journal of Theoretical PhysicsPublished 1 March 1992
Mladen Pavičić
Citations42
SJR quartileQ3
SJR score0.28
SNIP0.62
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Abstract
The bibliography contains 1851 references on axiomatic structures underlying quantum mechanics, with stress on varieties of algebraico-logical, probabilistic, and operational structures for which the term quantum logics is adopted. An index of about 250 keywords picked out from the titles is included and statistics about papers, journals, and authors are presented. Monographs and proceedings on the subject are noted.
Keywords
Computer SciencePhysics and Astronomy
Measures on the Closed Subspaces of a Hilbert Space
993 Citations1975Andrew M. Gleason
Annals of MathematicsOn an Algebraic Generalization of the Quantum Mechanical Formalism
907 Citations1934P. Jordan, J. v. Neumann +1 more
Communications in Mathematical PhysicsAn operational approach to quantum probability
903 Citations1970E. B. Davies, J. T. Lewis
Journal of Statistical PhysicsLogical reformulation of quantum mechanics. I. Foundations
441 Citations1988Roland Omn�s
Annals of MathematicsOn Inner Products in Linear, Metric Spaces
384 Citations1935P. Jordan, J. V. Neumann
Theory of Symmetric Lattices
357 Citations1970Fumitomo Maeda, Shûichirô Maeda
The Physicist’s Conception of Nature
208 Citations1973Jagdish Mehra
Journal of Mathematical PhysicsOperational Statistics. I. Basic Concepts
201 Citations1972David J. Foulis, C. H. Randall
Journal of Statistical PhysicsLogical reformulation of quantum mechanics. II. Interferences and the Einstein-Podolsky-Rosen experiment
166 Citations1988Roland Omn�s
Journal of Statistical PhysicsLogical reformulation of quantum mechanics. III. Classical limit and irreversibility
165 Citations1988Roland Omn�s
Journal of Mathematical PhysicsPrinciple of General <i>Q</i> Covariance
161 Citations1963David Finkelstein, J. M. Jauch +2 more
Contemporary Research in the Foundations and Philosophy of Quantum Theory
141 Citations1973C. A. Hooker
Pacific Journal of MathematicsOrthogonally additive and orthogonally increasing functions on vector spaces
141 Citations1975Stanley Gudder, D. Strawther
Communications in Mathematical PhysicsFundamental irreversibility and the concept of events
118 Citations1990Rudolf Haag
Mathematical Proceedings of the Cambridge Philosophical SocietyAn elementary proof of Gleason's theorem
117 Citations1985Roger Cooke, Michaël Keane +1 more
Fuzzy Sets and SystemsBrouwer-Zadeh posets and three-valued Łukasiewicz posets
101 Citations1989Gianpiero Cattaneo, Giuseppe Nisticò
Transactions of the American Mathematical SocietyOn Boolean algebras of projections and algebras of operators
100 Citations1955William G. Bade
Birkhäuser Basel eBooksLogical Structures Arising in Quantum Theory
87 Citations1990Simon Kochen, E Specker
Foundations of PhysicsRealism, operationalism, and quantum mechanics
83 Citations1983David J. Foulis, C. Piron +1 more
Publications of the Research Institute for Mathematical SciencesMeasures on infinite dimensional vector spaces
79 Citations1965Yasuo Umemura
Communications in Mathematical PhysicsConvex structures and operational quantum mechanics
72 Citations1973Stanley Gudder
Pacific Journal of MathematicsThe amalgamation property in equational classes of modular lattices
69 Citations1973George Grätzer, Bjàrni Jónsson +1 more
Bulletin of the Australian Mathematical SocietyQuantum logic as an implication algebra
68 Citations1970П. Д. Финч
Boston studies in the philosophy of scienceThe Labyrinth of Quantum Logics
59 Citations1974Bas C. van Fraassen
The aim of the present paper is to present a unified exposition of the main systems found in the literature, and to discuss and evaluate the main logical and philosophical theses and arguments which have concerned the subject of quantum logic.
Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BConditional probabilities in quantum mechanics. I.—Conditioning with respect to a single event
57 Citations1983Gianni Cassinelli, Nino Zanghı̀
Birkhäuser Boston eBooksThe Structure of Relatively Complemented Lattices
55 Citations1990R. P. Dilworth
Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BGeometry from quantum mechanics
54 Citations1980E. R. Caianiello
Journal of Symbolic LogicOrthomodularity is not elementary
51 Citations1984Robert Goldblatt
It is shown that the property of orthomodularity of the lattice of orthoclosed subspaces of a pre-Hilbert space ?? is not determined by any first-order properties of the relation I of orthogonality between vectors in b, and (CA, I) is an elementary substructure of ( I, I).
Algebra UniversalisCongruence modularity implies the Arguesian identity
50 Citations1976Ralph Freese, Bjàrni Jónsson
Journal of Symbolic LogicSequential method in quantum logic
50 Citations1980Hirokazu Nishimura
The main purpose of this paper is to alter this situation by presenting an axiomatization of quantum logic as natural and as elegant as possible, which further proof-theoretical study is to be based on.
Journal of Mathematical PhysicsFoundations of a quantum probability theory
50 Citations1975M. D. Srinivas
Journal of the Mathematical Society of JapanVon Neumann algebras and Boolean valued analysis
47 Citations1983Gaisi Takeuti
Bulletin of the London Mathematical SocietyA Completeness Criterion for Inner Product Spaces
42 Citations1987Jan Hamhalter, Pavel Pták
Transactions of the American Mathematical SocietyA noncommutative probability theory
38 Citations1978Stanley Gudder, R. L. Hudson
Physical Theory as Logico-Operational Structure
38 Citations1978C. A. Hooker
Journal of Mathematical PhysicsConstruction of the tensor product for the lattices of properties of physical entities
37 Citations1984Dirk Aerts
manuscripta mathematicaOn the definition of Hilbert space
35 Citations1977Herbert Gross, Hans A. Keller
International Journal of Theoretical PhysicsLogical foundation of quantum mechanics
35 Citations1980Ernst-Walther Stachow
Journal of Mathematical PhysicsObservables and the Field in Quantum Mechanics
29 Citations1971Stanley Gudder, C. Piron
Journal of Mathematical PhysicsHidden variables in quantum logic approach reexamined
29 Citations1991Jarosl aw Pykacz, Emilio Santos
Zeitschrift für Naturforschung ADie Quantentheorie der einfachen Alternative
28 Citations1958Carl Friedrich von Weizsäcker
Proceedings of the American Mathematical SocietyA characterization of inner product spaces
28 Citations1973R. A. Tapia
International Journal of Theoretical PhysicsClassical foundations of quantum logic
28 Citations1991Claudio Garola
Transactions of the American Mathematical SocietyDistributivity and perspectivity in orthomodular lattices
28 Citations1964Samuel S. Holland
Communications in Mathematical PhysicsRemarks on spectra of modular operators of von Neumann algebras
27 Citations1972Huzihiro Araki
International Journal of Theoretical PhysicsRealistic quantum probability
26 Citations1988Stanley Gudder
Communications in Mathematical PhysicsAttempt of an axiomatic foundation of quantum mechanics and more general theories. IV
25 Citations1968Günter Dähn
Foundations of PhysicsBrouwer-Zadeh logic and the operational approach to quantum mechanics
24 Citations1990Roberto Giuntini
International Journal of Theoretical PhysicsThe structure of projection-valued states: A generalization of Wigner's theorem
24 Citations1977Ron Wright
Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BConditional probabilities in quantum mechanics
24 Citations1984Gianni Cassinelli, Nino Zanghı̀
Studies in logic and the foundations of mathematicsLattice-Theoretic Approach to Projective and Affine Geometry
23 Citations1959Bjàrni Jónsson
Foundations of PhysicsRelative compatibility in conventional quantum mechanics
22 Citations1977Gary M. Hardegree
Journal of the Mathematical Society of JapanOn the representation of complemented modular lattices.
22 Citations1957Ichirô Amemiya
International Journal of Theoretical PhysicsCharacterization of quantum logics
20 Citations1980Pekka Lahti
Proceedings of the American Mathematical SocietyPerspectivity in projection lattices
20 Citations1965Peter Fillmore
Foundations of Physics LettersQuantum rules: an Effect can have more than one Operation
19 Citations1988Samuel L. Braunstein, Carlton M. Caves
Completeness of Quantum Logic
18 Citations1979Ernst-Walther Stachow
International Oil Spill Conference ProceedingsBOONE CREEK OIL SPILL
17 Citations1975Donald A. Schultz, L. B. Tebo
Canadian Journal of MathematicsVarieties of Orthomodular Lattices. II
17 Citations1972Günter Bruns, Gudrun Kalmbach
International Journal of Theoretical PhysicsCausality between preparation and registration processes in relativistic quantum theory
16 Citations1983Holger Neumann, Reinhard F. Werner
International Journal of Theoretical PhysicsNelson-brown motion: Some question marks
16 Citations1980Bogdan Mielnik, G�ran Tengstrand
Foundations of PhysicsStochastic quantum mechanics viewed from the language of manuals
16 Citations1990Franklin E. Schroeck, David J. Foulis
Journal of Philosophical LogicThe principle of excluded middle in quantum logic
16 Citations1978Peter Mittelstaedt, Ernst-Walther Stachow
From the fact that the principle of excluded middle can be confirmed for elementary propositions which are proved by quantum mechanical measurements, it is concluded that this principle is inherited by all finite compound propositions.
Foundations of Physics LettersEinstein?Podolsky?Rosen experiments: The structure of the probability space. II
15 Citations1988Matthias P. Kl�y
Reports on Mathematical PhysicsExpectation functionals of observables and counters
14 Citations1985Gottfried T. Rüttimann
International Journal of Theoretical PhysicsRelativity of topology and dynamics
14 Citations1984David Finkelstein, E. Benítez Rodríguez
Foundations of PhysicsSuperposition in quantum and classical mechanics
13 Citations1990M. K. Bennett, David J. Foulis
Elsevier eBooksANOTHER NONSTANDARD QUANTUM LOGIC (AND HOW I FOUND IT)
13 Citations1978Richard J. Greechie
International Journal of Theoretical PhysicsBanach spaces of weights on quasimanuals
12 Citations1985Thurlow A. Cook
Classical and Quantum Descriptions
12 Citations1973Carl Friedrich von Weizsäcker
This paper takes a particular approach in starting from the idea of a quantum logic, not a peculiar ‘empirical’ logic, but a specification of a general logic of temporal statements, that is of statements on facts and possibilities.
International Journal of Theoretical PhysicsConditional expectations, conditional distributions, anda posteriori ensembles in generalized probability theory
12 Citations1988Werner Stulpe
Communications in Mathematical PhysicsA superposition principle in quantum logics
12 Citations1976Sylvia Pulmannová
Foundations of PhysicsFinitely additive states and completeness of inner product spaces
12 Citations1990Anatolij Dvurečenskij, Tibor Neubrunn +1 more
Journal of Symbolic LogicModal propositional logic on an orthomodular basis. I
12 Citations1974Louis Herman, Robert Piziak
International Journal of Theoretical PhysicsTensor product of frame manuals
12 Citations1990Alexander Wilce
International Journal of Theoretical PhysicsState automorphisms in axiomatic quantum mechanics
11 Citations1973Stanley Gudder
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