10,754 research outputs found

    Information and The Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

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    In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.Comment: 20 pages, two figures, last version. Section 4 is replaced by a new argument. Other sections are improved. An appendix and new references are adde

    A Field-theoretical Interpretation of the Holographic Renormalization Group

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    A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Similarly we discuss how in four dimensions the holographic C function is related to a conjectured field-theoretical C function. The scheme dependence of the holographic RG due to the possible presence of finite local counterterms is discussed in detail, as well as its implications for the holographic C function. We also discuss issues special to the situation when mass deformations are present. Furthermore we suggest that the holographic RG equation may also be obtained from a bulk diffeomorphism which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected, paragraph added to section

    Finiteness and children with specific language impairment: an exploratory study

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    Children with specific language impairment (SLI) are well known for their difficulties in mastering the inflectional paradigms; in the case of learning German they also have problems with the appropriate verb position, in particular with the verb in second position. This paper explores the possibilities of applying a broader concept of finiteness to data from children with SLI in order to put their deficits, or rather their skills, into a wider perspective. The concept, as developed by Klein (1998, 2000), suggests that finiteness is tied to the assertion that a certain state of affairs is valid with regard to some topic time; that is, finiteness relates the propositional content to the topic component. Its realization involves the interaction of various grammatical devices and, possibly, lexical means like temporal adverbs. Furthermore, in the acquisition of finiteness it has been found that scope particles play a major role in both first- and second-language learning. The purpose of this paper is to analyze to what extent three German-learning children with SLI have mastered these grammatical and lexical means and to pinpoint the phase in the development of finiteness they have reached. The data to be examined are mostly narrative and taken from conversations and experiments. It will be shown that each child chooses a different developmental path to come to grips with the interaction of these devices

    Intuitionistic logic and its philosophy

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    Beyond cash-additive risk measures: when changing the num\'{e}raire fails

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    We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a risk-free bond, on the grounds that the general case can be reduced to the cash-additive case by a change of numeraire. However, discounting does not work in all financially relevant situations, typically when the eligible asset is a defaultable bond. In this paper we fill this gap allowing for general eligible assets. We provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures based on Value-at-Risk and Tail Value-at-Risk on LpL^p spaces, as well as to shortfall risk measures on Orlicz spaces. We pay special attention to the property of cash subadditivity, which has been recently proposed as an alternative to cash additivity to deal with defaultable bonds. For important examples, we provide characterizations of cash subadditivity and show that, when the eligible asset is a defaultable bond, cash subadditivity is the exception rather than the rule. Finally, we consider the situation where the eligible asset is not liquidly traded and the pricing rule is no longer linear. We establish when the resulting risk measures are quasiconvex and show that cash subadditivity is only compatible with continuous pricing rules

    Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory

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    This paper focuses on a three-parameter deformation of N=4 Yang-Mills that breaks all the supersymmetry in the theory. We show that the resulting non-supersymmetric gauge theory is scale invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in light-cone perturbation theory.Comment: 13 pages, 1 figure; v2: minor correction
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