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1.
Gianpiero Cattaneo Alberto Leporati Roberto Leporini 《International Journal of Theoretical Physics》2004,43(7-8):1769-1791
We introduce some conservative gates for finite-valued logics which are able to realize all the main connectives of the many-valued logics of ?ukasiewicz, the MV-algebras of Chang and Brower–Zadeh algebras. After a brief exposition of the motivations for this work, the gates are defined and their properties are explored. Finally, a possible quantum realization of them is proposed, using three techniques: a “brute force” method--an extension of the Conditional Quantum Control argument, and a new technique which we call the Constants Method. For all these techniques, the unitary operator which describes the gate is a sum of local operators. 相似文献
2.
Gianpiero Cattaneo Giuseppe Nisticó 《International Journal of Theoretical Physics》1992,31(10):1873-1898
We give a criterion to compare the physical content of different mathematical structures derived from a preparation-question structure. Then this criterion is used in order to compare the physical content of the (Jauch-Piron's) property lattice with the physical content of the poset of testable properties. We prove that for complete preparation-question structures these two structures carry the same physical content; moreover the set of testable properties has the algebraic structure of the Brouwer-Zadeh lattice. For more general preparation-question structures the physical content of the poset of testable property can be larger than that of the property lattice. Physically relevant examples of the possible cases are given. 相似文献
3.
Alberto S. Cattaneo 《Communications in Mathematical Physics》1997,189(3):795-828
In the context of the Batalin–Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander–Conway polynomial. The three-dimensional case
is analyzed explicitly, and it is proved to be anomaly free. Moreover, at the second order in perturbation theory, a new formula
for the second coefficient of the Alexander–Conway polynomial is obtained. An account on the higher-dimensional generalizations
is also given.
Received: 2 October 1996 / Accepted: 21 March 1997 相似文献
4.
5.
6.
Some algebraic structures determined by the class (þ) of all effects of a Hilbert space þ and by some subclasses of (þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that (þ
n
)(n<) has such a structure], Brouwer-Zadeh
*
posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh
3
posets which are both de Morgan and
*.It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ
3
poset. An -preclusivity relation on the set of all vectors of þ is introduced, and it is shown that it satisfies the regularity condition also for [1/2, 1]. 相似文献
7.
Gianpiero Cattaneo 《International Journal of Theoretical Physics》1993,32(10):1709-1734
A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operatorsF on a Hilbert space such that, 0¦F2) the role played by orthomodular posets with respect to orthogonal projections (corresponding to sharp effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (afuzzy-like and anintuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ* posets, and BZ3 posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed. 相似文献
8.
E.?DesimoniEmail author B.?Brunetti R.?Cattaneo 《Accreditation and quality assurance》2004,9(8):445-449
Considering the uncertainty of measurement when assessing compliance with reference values given in compositional specifications and statutory limits is still a controversial matter. In theory, assessing compliance requires considering both type I (false positive) and type II (false negative) errors. The more the concentration of the analyte in the sample under investigation is close to the allowed concentration limit, the more critical it is to consider both types of errors. This paper describes how this could be done. The matter is discussed in the light of the most recent literature information. 相似文献
9.
Alberto S. Cattaneo Pavel Mnev Nicolai Reshetikhin 《Communications in Mathematical Physics》2014,332(2):535-603
In this paper we extend the classical BV framework to gauge theories on spacetime manifolds with boundary. In particular, we connect the BV construction in the bulk with the BFV construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners. We present several examples including electrodynamics, Yang-Mills theory and topological field theories coming from the AKSZ construction, in particular, the Chern-Simons theory, the BF theory, and the Poisson sigma model. This paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing. 相似文献
10.
Gianpiero Cattaneo 《International Journal of Theoretical Physics》1992,31(9):1573-1597
The partial ordered structure which plays for unsharp quantum mechanics the same role of orthomodular lattices for ordinary quantum mechanics is introduced. Differently from the unsharp case, in which one can identify quantum propositions (i.e., Hilbert space subspaces) with yes-no devices (i.e., orthogonal projections) they are tested by, in the unsharp case this identification is broken down: every quantum generalized proposition (i.e., pair of mutually orthogonal subspaces) is tested by many different yes-no devices (i.e., Hilbert space effects). The set of all quantum effects has a structure of Brouwer-Zadeh poset, canonically embeddable in a (minimal) Brouwer-Zadeh lattice, whereas the set of all quantum generalized propositions has a structure of Brouwer-Zadeh complete lattice.A Brouwer-Zadeh poset is defined as a partially ordered structure equipped with two nonusual orthocomplementations: a regular degenerate (Zadeh or fuzzy-like) one and a weak (Brouwer or intuitionistic-like) one linked by an interconnection rule. Using these two orthocomplementations it is possible to introduce the two modal-like operators of necessity and possibility. 相似文献