Poisson Spaces with a Transition Probability

DOI10.1142/S0129055X97000038zbMath0892.46083arXivquant-ph/9603005OpenAlexW3099330539MaRDI QIDQ3127472

Nicolaas P. Landsman

Publication date: 20 July 1998

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/9603005

zbMATH Keywords

transition probabilityPoisson spacespure state spaces of \(C^\ast\)-algebras

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05) Geometry and quantization, symplectic methods (81S10) Applications of functional analysis in quantum physics (46N50) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10)

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Cites Work

• The local structure of Poisson manifolds
• Locally compact division rings
• Jordan axioms for C*-algebras
• On a characterization of the state space of quantum mechanics
• State space of C*-algebras
• Pure states as a dual object for C*-algebras
• Stratified symplectic spaces and reduction
• Complements to various Stone-Weierstrass theorems for \(C^*\)-algebras and a theorem of Shultz
• Jordan \(C^*\)-algebras
• A Gelfand-Neumark theorem for Jordan algebras
• State spaces of Jordan algebras
• Zur Begründung der projektiven Geometrie
• Axioms for non-relativistic quantum mechanics
• Unitary operators in \(C^ *\)-algebras
• Geometry of quantum states
• Some basic concepts of algebraic quantum theory
• Theory of filters
• Postulates for general quantum mechanics
• CLASSICAL BEHAVIOR IN QUANTUM MECHANICS: A TRANSITION PROBABILITY APPROACH
• Quantum mechanics as an infinite-dimensional Hamiltonian system with uncertainty structure: Part I
• Transition probability spaces
• On Non-Commutative Spectral Theory and Jordan Algebras
• A FUNCTIONAL REPRESENTATION FOR NON-COMMUTATIVE C*-ALGEBRAS
• Characterization of hilbert spaces by orthomodular spaces
• Duality of observables and generators in classical and quantum mechnics
• Orthomodularity in infinite dimensions; a theorem of M. Solèr
• Complex Coordinates and Quantum Mechanics
• A remark on Piron's paper

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