共查询到20条相似文献,搜索用时 11 毫秒
1.
Vladimir Müller Pavel Pták Josef Tkadlec 《International Journal of Theoretical Physics》1992,31(5):843-854
LetL be a concrete (=set-representable) quantum logic. Letn be a natural number (or, more generally, a cardinal). We say thatL admits intrinsic coverings of the ordern, and writeL
C
n
, if for any pairA, BL we can find a collection {C
i
iI}, where cardI<n andC
i
L for anyiI, such thatA B=
il
C
i
. Thus, in a certain sense, ifLC
n
, then the rate of noncompatibility of an arbitrary pairA,BL is less than a given numbern. In this paper we first consider general and combinatorial properties of logics ofC
n
and exhibit typical examples. In particular, for a givenn we construct examples ofL
C
n+1\C
n
. Further, we discuss the relation of the classesC
n
to other classes of logics important within the quantum theories (e.g., we discover the interesting relation to the class of logics which have an abundance of Jauch-Piron states). We then consider conditions on which a class of concrete logics reduce to Boolean algebras. We conclude with some open questions. 相似文献
2.
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
3.
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
4.
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
5.
6.
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
7.
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
8.
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
9.
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
10.
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
11.
12.
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
13.
Summary Two-particle quantum systems with spin can be simulated by classical automata described by graphs. These graphs are associated with nondistributive property lattices of these quantum systems. We emphasize that to non-local properties of a quantum system being in a certain eigenstate of the permutation operator there correspond merely some additional vertices in the graph which have nothing nonlocal in their nature. This leads to the possibility of violating Bell's inequalities in classical systems described by graphs (see Section 6) without violating relativity theory.The subjective interpretation of quantum mechanics of von Neumann, London, and Bauer can be connected with the Boolean nature of mind grasping the non-Boolean nature of the world, which results in the projection postulate: wave packet reduction. A simple example is given for a two-particle system with spin. 相似文献
14.
Boolean transfer from coherent quantum logics to quantum logics with continuous superselection rules
Hirokazu Nishimura 《International Journal of Theoretical Physics》1992,31(5):855-869
Quantum logics with continuous superselection rules are shown to be Booleanvalued coherent quantum logics. Since modern set theory provides a transfer principle from standard mathematics to Boolean-valued mathematics, this makes it possible to transfer automatically well-known results on coherent quantum logics to quantum logics with continuous superselection rules. Many illustrations are given. 相似文献
15.
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
16.
The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, we investigate the relationship between unsharp orthoalgebras, generalized MV algebras, and orthomodular lattices. 相似文献
17.
Roman R. Zapatrin 《International Journal of Theoretical Physics》1994,33(1):213-224
The arithmetical tools based on Boolean matrices are described. They are applied to finite ortholattices to decompose them into products and sums, and to check atomisticity and orthomodularity. 相似文献
18.
We offer a variant of the intrinsic definition of compatibility in logics. We shown that any compatible subset can be embedded into a Boolean -algebra, we show how the algebra is constructed, and we demonstrate that our definition cannot be weakened unless we put additional assumptions on the logic. 相似文献
19.
Antonio Zecca 《International Journal of Theoretical Physics》1992,31(8):1363-1370
The notion of dynamical semigroup is introduced in the quantum logic scheme on the set of the states. Under suitable nonempty mathematical assumptions it is shown that a Heisenberg picture exists equivalent to the Schrödinger one and having many aspects similar to those of the Hilbert case. 相似文献
20.
Gottfried T. Rüttimann 《International Journal of Theoretical Physics》1994,33(1):149-156
The notion of a superposition of a set of states and that of a Jauch-Piron state are geometrically interpreted in the context of the facial structure of the state space of a finite quantum logic. 相似文献