Remarks on representation of fuzzy quantum posets
Remarks on tensor products and their applications in quantum theory I. General considerations
Remarks on tensor proucts and their applications in quantum theory - II. Spectral properties
Remarks on the order for quantum observables
Representation of observables in quantum mechanical models
Representation theorem for convex effect algebras
Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
Seeable matter; unseeable antimatter
The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra , an interpretation is developed that suggests that this seeable universe is not the whole universe; there is an unseeable part of the universe composed of antimatter galaxies and stuff, and an extra 6 dimensions of space (also unseeable) linking the matter side to the antimatter—at the very least.
Semiobservables on quantum logics
Some distributivities in GBbi-QRs characterizing Boolean rings
This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.
Spaces of observables
Spectral resolutions for -complete lattice effect algebras
State space properties of finite logics
Statistical maps. I: Basic properties
Statistical maps. II: Operational random variables and the Bell phenomenon
Sum of observables in fuzzy quantum spaces
We introduce the sum of observables in fuzzy quantum spaces which generalize the Kolmogorov probability space using the ideas of fuzzy set theory.
Superpositions of states and a representation theorem
Supporting sequences of pure states on JB algebras
We show that any sequence of mutually orthogonal pure states on a JB algebra A such that forms an almost discrete sequence in the relative topology induced by the primitive ideal space of A admits a sequence consisting of positive, norm one, elements of A with pairwise orthogonal supports which is supporting for in the sense of for all n. Moreover, if A is separable then can be taken such that is uniquely determined by the biorthogonality condition . Consequences of this result improving...
Symmetric difference in orthomodular lattices
Symmetric difference on orthomodular lattices and -valued states
The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space.