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Following Birkhoff and von Neumann , quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections ...
structure, the quasi- lattice (\({\mathfrak{I}}\)- lattice ), which can be modeled by an algebraic structure built in quasi-set theory \({\mathfrak{Q}}\) . This structure is non distributive and involve ...
AbstractThe aim of the present paper is to study lattice outer measures on an unsharp quantum logic, viz. a difference poset P associated with a monotone function μ defined on a sub-difference poset ...
In this article we give new examples of models in boundary quantum field theory , i.e. local time-translation covariant nets of von Neumann algebras , using a recent construction of Longo and Witten ...
-commutative filtration of a von Neumann algebra as well as those employed in quantum stochastic theory of the canonical anticommutation relations (CAR) and the canonical commutation relations (CCR) (cf. [4], [9 ...
construction of the spatially-localized von Neumann algebras of time-zero fields in the time gauge in representations associated with scaling limits of Gibbs states of the Kogut-Susskind Hamiltonian. We relate ...
for dealing with real Jordan operator algebras . From a measure- theoretic standpoint, this setting contains a generalization of noncom- mutative measure and probability theory on the projection lattices of von ...
Probability and Related Topics , 1998 , vol. 1 4 (pg. 663 - 670 ) OpenURL Placeholder Text WorldCat 2 Araki H. . A lattice of von Neumann algebras associated with the quantum theory of a free Bose field ...
is that of associating graphs to density matrices and measuring the complexity of the graphs in terms of the von Neumman entropy of the corresponding density matrices. This in turn is based on the mapping between quantum ...
finitely additive) then ωPr is a normal (respectively, non-normal) quantum state. Gleason’s theorem has been extended to quite general von Neumann algebras , including the Type III algebras encountered ...
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