Reichenbach's Common Cause Principle in Algebraic Quantum Field Theory with Locally Finite Degrees of Freedom

In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A and B supported in spacelike separated double cones O(a) and O(b), respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of O(a) and O(b) and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models

Local Operations and Completely Positive Maps in Algebraic Quantum Field Theory

Einstein introduced the locality principle which states that all physical effect in some finite space-time region does not influence its space-like separated finite region. Recently, in algebraic quantum field theory, R\'{e}dei captured the idea of the locality principle by the notion of operational separability. The operation in operational separability is performed in some finite space-time region, and leaves unchanged the state in its space-like separated finite space-time region. This operation is defined with a completely positive map. In the present paper, we justify using a completely positive map as a local operation in algebraic quantum field theory, and show that this local operation can be approximately written with Kraus operators under the funnel property

Remarks on Causality in Relativistic Quantum Field Theory

It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras \cA(V_1),\cA(V_2) associated with spacelike separated spacetime regions $V_1,V_2$ have a (Reichenbachian) common cause located in the union of the backward light cones of $V_1$ and $V_2$. Further comments on causality and independence in quantum field theory are made.Comment: 10 pages, Latex, Quantum Structures 2002 Conference Proceedings submission. Minor revision of the order of definitions on p.

Noncommutative causality in algebraic quantum field theory

In the paper it will be argued that embracing noncommuting common causes in the causal explanation of quantum correlations in algebraic quantum field theory has the following two beneficial consequences: it helps (i) to maintain the validity of Reichenbach's Common Causal Principle and (ii) to provide a local common causal explanation for a set of correlations violating the Bell inequality

The antioxidant capacity of sea buckthorn (Hippophae rhamnoides L.) berries depends on the genotype and harvest time

Berries of sea buckthorn (Hippophae rhamnoides L.) are characterized by increasing popularity due to their presumable health-effects. The aim of this study was to compare the antioxidant capacity and total polyphenolic content in the berries of six Hungarian grown sea buckthorn genotypes and characterize the genetic variability in this trait. The harvest time of sea buckthorn berries affects the antioxidant capacity and total phenolic contents in berries of three popular cultivars of German origin. Berries harvested in October had higher antioxidant capacity compared with those harvested one month later. The extent of the difference was genotype-specific. Our analysis revealed a nearly 3-fold difference between the lowest and highest antioxidant capacities of the 6 tested genotypes with ‘Leikora’ showing the highest ferric reducing antioxidant power and total phenolic content. The TEAC values ranged between 1.76 and 3.13 mmol Trolox/100g fresh weight with Pető 1 and ‘Frugana’ having the highest values. The results presented in this study demonstrated that Hippophae rhamnoides berries possess in vitro antioxidant activity strongly determined by genotype but also influenced by harvest time

Markov semigroups, monoids, and groups

A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown to be equivalent. Various interesting examples are presented, including an example of a non-Markov monoid that nevertheless admits a regular language of unique representatives over any generating set. It is shown that all finitely generated commutative semigroups are strongly Markov, but that finitely generated subsemigroups of virtually abelian or polycyclic groups need not be. Potential connections with word-hyperbolic semigroups are investigated. A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finite-index subsemigroups and extensions. Several questions are posed.Comment: 40 pages; 3 figure

Extended Representations of Observables and States for a Noncontextual Reinterpretation of QM

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR model containing a more complete mathematical representation of the basic entities of the model. We also extend the model to mixtures showing that the mathematical representations of proper mixtures does not coincide with the mathematical representation of mixtures provided by QM, while the representation of improper mixtures does. This feature of the ESR model entails that some interpretative problems raising in QM when dealing with mixtures are avoided. From an empirical point of view the predictions of the ESR model depend on some parameters which may be such that they are very close to the predictions of QM in most cases. But the nonstandard representation of proper mixtures allows us to propose the scheme of an experiment that could check whether the predictions of QM or the predictions of the ESR model are correct.Comment: 17 pages, standard latex. Extensively revised versio

Semantic distillation: a method for clustering objects by their contextual specificity

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence, Springer-Verla

The antioxidant capacity of sea buckthorn (Hippophae rhamnoides L.) berries depends on the genotype and harvest time

Berries of sea buckthorn (Hippophae rhamnoides L.) are characterized by increasing popularity due to their presumable healtheffects. The aim of this study was to compare the antioxidant capacity and total polyphenolic content in the berries of six Hungarian grown sea buckthorn genotypes and characterize the genetic variability in this trait. The harvest time of sea buckthorn berries affects the antioxidant capacity and total phenolic contents in berries of three popular cultivars of German origin. Berries harvested in October had higher antioxidant capacity compared with those harvested one month later. The extent of the difference was genotype-specific. Our analysis revealed a nearly 3-fold difference between the lowest and highest antioxidant capacities of the 6 tested genotypes with ‘Leikora’ showing the highest ferric reducing antioxidant power and total phenolic content. The TEAC values ranged between 1.76 and 3.13 mmol Trolox/100g fresh weight with Pető 1 and ‘Frugana’ having the highest values. The results presented in this study demonstrated that Hippophae rhamnoides berries possess in vitro antioxidant activity strongly determined by genotype but also influenced by harvest time