Observables, states, and symmetries in the context of CB-effect algebras

DOI10.1016/S0034-4877(07)80143-1zbMath1140.81007MaRDI QIDQ2477373

David J. Foulis

Publication date: 13 March 2008

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

symmetryobservableBoolean algebrastateprobability measureeffect algebracompression base\(\sigma\)-observablePOV-measure\(\sigma\)-stateBorel observableCB-effect algebraconditioned stateeffect-algebra morphismmonotone \(\sigma\)-complete

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Vector-valued set functions, measures and integrals (28B05) Positive linear operators and order-bounded operators (47B65) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Linear operators in (C^*)- or von Neumann algebras (47C15)

Related Items (7)

Logical connectives on lattice effect algebras ⋮ Hilbert space effect-representations of effect algebras ⋮ Equational characterization for two-valued states in orthomodular quantum systems ⋮ Two-valued states on Baer \(^\ast\)-semigroups ⋮ Logical approach for two-valued states on quantum systems ⋮ Spectral automorphisms in CB-effect algebras ⋮ Comment on ‘The operational foundations of PT-symmetric and quasi-Hermitian quantum theory’

Cites Work

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• Effect algebras and unsharp quantum logics.
• Quantum information processing, operational quantum logic, convexity, and the foundations of physics
• Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
• Additivity of integrals on generalized measure spaces
• The structure of projection-valued states: A generalization of Wigner's theorem
• States on causal logic
• Regularity in quantum logic
• Interval and scale effect algebras
• Coexistent observables and effects in quantum mechanics
• Subdirect decompositions of lattice effect algebras
• Generalization of blocks for \(D\)-lattices and lattice-ordered effect algebras
• Convex effect algebras, state ordered effect algebras, and ordered linear spaces
• Compressible effect algebras
• Reasoning in quantum theory. Sharp and unsharp quantum logics.
• The center of an effect algebra
• Convex and linear effect algebras
• Extensions of convexity models
• ⊥-order automorphisms of Hilbert space effect algebras: The two-dimensional case
• Algebraic Analysis of Many Valued Logics
• On the infimum of quantum effects
• Nonstandard scalar quantum fields
• Symmetry Groups in Quantum Mechanics and the Theorem of Wigner on the Symmetry Transformations
• FUZZY PROBABILITY THEORY
• Coexistent observables and effects in a convexity approach
• The logic of causally closed spacetime subsets
• Compressions on partially ordered abelian groups
• An Extension of Classical Measure Theory
• COMPRESSION BASES IN EFFECT ALGEBRAS
• The Theory of Representation for Boolean Algebras

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