共查询到20条相似文献,搜索用时 15 毫秒
1.
V. Müller 《International Journal of Theoretical Physics》1993,32(3):433-442
We exhibit an example of a concrete (=set-representable) quantum logic which is not a Boolean algebra such that every state on it is Jauch-Piron. This gives a negative answer to a problem raised by Navara and Pták. Further we show that such an example does not exist in the class of complete (i.e., closed under arbitrary disjoint unions) concrete logics. 相似文献
2.
Sylvia Pulmannová 《International Journal of Theoretical Physics》1990,29(5):455-460
Relations between transition amplitude spaces and quantum logics are studied. It is shown that transition amplitude spaces correspond to quantum logics with rich enough sets of vector-valued states. 相似文献
3.
We study conditions under which the group of symmetries of a quantum logic is isomorphic to the group of symmetries on certain subsets of the state space of the logic. The notions of Jordan–Hahn decomposition and ultrafulness of the set of states under consideration play a fundamental role in these investigations. They are used to establish a connection between the elements of the logic and the weak1-exposed points or extreme points of the unit interval of the Banach dual of the signed state space. The results are then interpreted in the standard logic of quantum mechanics. 相似文献
4.
Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue. 相似文献
5.
David Finkelstein 《International Journal of Theoretical Physics》1992,31(9):1627-1638
Until now quantum logics has been first-order, but physics requires higher-order logics. We construct a natural higher-order languageQ for quantum physics.Q is a finitistic logic based on Peano set theory and Grassmann algebra. Higher-order predicates are identified with their extensions, higher-rank sets. QAND and QOR (the AND and OR ofQ) are naturally noncommutative but reduce to the commutative lattice operations for the first-order part of the language. We form higher-order predicates and sets by a setting operator similar to Peano'st that forms a simple extensort = }} from any extensor. In a note added in proof, we correctQ so that a bond like {{, }} between two fermions and is a quasiboson, as the application to lattice chromodynamics strongly suggests. 相似文献
6.
Stochastic processes on quantum logics are defined and the properties of a Brownian motion process are studied. A stochastic integral with respect to this Brownian motion process is constructed. 相似文献
7.
Maria Luisa Dalla Chiara 《International Journal of Theoretical Physics》1995,34(8):1331-1336
The event-structure of a state-event system, containing unsharp elements, can be described either as aregular involutive bounded poset, or alternatively as anunsharp orthoalgebra (called alsodifference poset oreffect algebra). Such structures give rise to different forms ofunsharp quantum logics. 相似文献
8.
Radko Mesiar 《International Journal of Theoretical Physics》1994,33(7):1417-1425
Families of fuzzy subsets equipped by continuous fuzzy connectives which are quantum logics in a traditional sense are studied. As a special case, we obtain a generalized fuzzy quantum logic introduced recently by Pykacz. 相似文献
9.
We define two types of convergence for observables on a quantum logic which we call M-weak and uniform M-weak convergence. These convergence modes correspond to weak convergence of probability measures. They are motivated by the idea that two (in general unbounded) observables are close if bounded functions of them are close. We show that M-weak and uniform M-weak convergence generalize strong resolvent and norm resolvent convergence for self-adjoint operators on a Hilbert space. Also, these types of convergence strengthen the weak operator convergence and operator norm convergence of bounded self-adjoint operators on a Hilbert space. Finally, we consider spectral perturbation by showing that the spectra of approximating observables approach the spectrum of the limit in a certain sense. 相似文献
10.
Paweł Kruszyński 《Reports on Mathematical Physics》1980,17(1):59-61
A correct proof of the theorem stated in [4] is given. The problem of equivalence between theorems of Dye and Gleason is formulated. 相似文献
11.
Sylvia Pulmannová 《International Journal of Theoretical Physics》1996,35(11):2309-2319
Starting with a quantum logic (a -orthomodular poset)L, a set of probabilistically motivated axioms is suggested to identifyL with a standard quantum logicL(H) of all closed linear subspaces of a complex, separable, infinite-dimensional Hilbert space. Attention is paid to recent results in this field. 相似文献
12.
Paweł Kruszyński 《Reports on Mathematical Physics》1976,10(2):213-217
Automorphisms of quantum logics are studied. If a quantum logic, i.e. an orthomodular complete lattice of propositions concerning a physical system, is represented as the lattice of all projections in a von Neumann algebra, then each automorphism of the logic can be represented as a Jordan automorphism in the algebra. Groups of transformations of a physical system are represented as groups of 1-automorphisms in a von Neumann algebra, provided certain continuity conditions are fulfilled. 相似文献
13.
14.
S. Pulmannovà 《International Journal of Theoretical Physics》1983,22(9):837-850
A quantum logic is a couple (L, M), whereL is a logic andM is a quite full set of states onL. A tensor product in the category of quantum logics is defined and a comparison with the definition of free orthodistributive product of orthomodular σ lattices is given. Several physically important cases are treated. 相似文献
15.
S. Pulmannová 《Foundations of Physics》1981,11(1-2):127-136
Two postulates concerning observables on a quantum logic are formulated. By Postulate 1 compatibility of observables is defined by the strong topology on the set of observables. Postulate 2 requires that the range of the sum of observables ought to be contained in the smallestC-closed sublogic generated by their ranges. It is shown that the Hilbert space logicL(H) satisfies the two postulates. A theorem on the connection between joint distributions of types 1 and 2 on the logic satisfying Postulate 2 is proved. 相似文献
16.
The idea of computational complementarity is developed further. A special class of macroscopic automata to imitate quantum and classical systems is described. The simplest automaton imitating a spin-1/2 particle is completely considered. 相似文献
17.
S. Pulmannová 《International Journal of Theoretical Physics》1977,16(9):681-688
A symmetry in the quantum logic (L, M) is defined as a pair of bijections :L L andv :M M such that the probabilities are preserved. Some properties of the symmetries are investigated. 相似文献
18.
We take up the question of when a state (= -additive measure) on the product of logics (=-orthomodular posets) depends on at most countably many coordinates. We show that it is always so provided there are no real-measurable cardinals. The manner of dependence is a kind of convex combination. We derive some consequences of the latter statement. 相似文献
19.
S. Pulmannová 《International Journal of Theoretical Physics》1978,17(9):665-675
A joint distribution of a set of observables on a quantum logic in a statem is defined and its properties are derived. It is shown that if the joint distribution exists, then the observables can be represented in the statem by a set of commuting operators on a Hilbert space. 相似文献