Bell inequality and common causal explanation in algebraic quantum field theory

Bell inequalities, understood as constraints between classical conditional probabilities, can be derived from a set of assumptions representing a common causal explanation of classical correlations. A similar derivation, however, is not known for Bell inequalities in algebraic quantum field theories establishing constraints for the expectation of specific linear combinations of projections in a quantum state. In the paper we address the question as to whether a 'common causal justification' of these non-classical Bell inequalities is possible. We will show that although the classical notion of common causal explanation can readily be generalized for the non-classical case, the Bell inequalities used in quantum theories cannot be derived from these non-classical common causes. Just the opposite is true: for a set of correlations there can be given a non-classical common causal explanation even if they violate the Bell inequalities. This shows that the range of common causal explanations in the non-classical case is wider than that restricted by the Bell inequalities

Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B

Algebrai módszerek kvantumtérelméleti modellekben = Algebraic methods in models of quantum field theory

Kutatásaink a kvantumtérelmélet, a kvantumgruppoidok és a kategóriaelmélet határterületén új fogalmak bevezetésével és új összefüggések feltárásával gazdagította a terület szakidodalmát. Főbb eredményeink: Bevezetve a nemkommutatív közös ok fogalmát megmutattuk, hogy a Bell-egyenlőtlenséget sértő korrelációhalmaz is föloldható egyetlen lokális, nemkommutatív közös okkal. A Hopf-ciklikus (ko)homológia elmélet a nem kommutatív geometriai szimmetriák leírására alkalmas. A korábbi megközelítésekkel szemben egy alapvetően új kategóriaelméleti tárgyalást vezettünk be, amely magában foglalja azokat a realisztikusabb modelleket is, melyek szimmetriáját Hopf algebroid írja le. Olyan monádokat vizsgáltunk, melyek Eilenberg-Moore kategóriája rendelkezik a gyenge bialgebrák modulus kategóriáinak jellemző vonásaival: monoidális és a felejtő funktor szeparábilis Frobenius. Számos gyenge Hopf algebrákra vonatkozó eredmény kiterjesztése rájuk azt mutatja, hogy ez a megfelelő általánosítás a monádok körében. Bevezettük a ferde monoidális kategória fogalmát és bebizonyítottuk, hogy egy R gyűrű feletti bialgebroidok ekvivalensek az (egyoldali!) R-modulusok kategóriáján definiált zárt, ferde monoidális struktúrákkal. | Our research activity in the areas of quantum field theory, quantum groupoids and category theory has resulted in new concepts and revealed new relationships which we presented in 16 scientific publications. The main results are the following. By introducing the notion of non-commutative common cause we have shown that a joint local non-commutative common cause can explain a set of correlations even if it violates the Bell inequalities. Hopf-cyclic (co)homology theory is capable to describe the symmetries in non-commutative geometry. We invented a novel categorical treatment which, in contrast to earlier approaches, incorporates more realistic models possessing Hopf algebroid symmetries. We studied monads whose Eilenberg-Moore category bears the characteristic properties of module categories over a weak bialgebra: it is monoidal and its forgetful functor is separable Frobenius. Extending to them a number of results on weak bialgebras justifies that they provide the proper generalization to the monadic setting. We have introduced the notion of skew monoidal categories and proved that the closed skew monoidal structures on the category of (one-sided!) R-modules are precisely the bialgebroids over the ring R

Alacsony dimenziós kvantumtérelméleti modellek vizsgálata = Investigations in low dimensional quantum field theory

1. 2d integrálható modellek Termodinamikai Bethe ansatz és integrálegyenlet technikával véges méret spektrumot határoztunk meg. O(N)-modellek kontinuum limesz konstrukciójában megadtuk a rácskorrekciók eltűnésének rácsállandó-függését. O(3)-modellbeli ''hadronikus'' struktúra-függvényre kis Bjorken-x-re egzakt alakot vezettünk le. 2 Szimmetriastruktúrák és Calogero modellek Megadtuk a WZNW-modellek Poisson-Lie szimmetriáit generáló momentum-leképzést, a dinamikai Yang-Baxter egyenlet általánositását, a Calogero modell inekvivalens kvantálásait. Megmutattuk, hogy dinamikai r-mátrix konstrukciói spin Calogero modelleknek Lie csoporton való szabad mozgás hamiltoni redukciói. Negativ görbületű Riemann szimmetrikus téren szabad mozgás hamiltoni redukciója spin Calogero modellre vezet. 3.Spinláncok és rácselméletek Megmutattuk, hogy az XX-láncnál az energiáram, Heisenberg-láncnál a csatolások kváziperiodikus perturbációja az összefonódottságot növeli, s hogy kvantumspinláncok eltolásinvariáns állapotaira vonatkozó nulla entrópia-sűrűség sejtés éles. MC szimulációval azt találtuk, hogy a 4d Ising modell kontinuum limesze triviális, de a konvergencia nagyon lassú. 4.Kvantumgrupoidok 2-es mélységű algebrabővitéseket jellemeztünk bialgebroidokkal, melyek balanszirozott esetben a Galois-csoport analógjai. Bevezettük a Hopf algebroidok fogalmát, tanulmányoztuk szerepüket hasadt algebra-bővitésekben, Hopf-Galois kiterjesztésekben és nem-kommutativ geometrában. | 1. 2d integrable models Finite volume spectra are given using thermal Bethe ansatz and integral equations. The decay form of lattice artifacts is established in the continuum limit construction of O(N)-models. The exact small (Bjorken) x behaviour of the 'hadronic' structure function in the O(3)-model was derived. 2.Symmetry structures and Calogero models The momentum map, the generator of Poisson-Lie symmetries in WZNW models was given, the dynamical Yang-Baxter equation was generalized. Inequivalent quantizations of Calogero model were given. Dynamical r-matrix construction of spin Calogero model is shown to be the Hamiltonian reduction of free motion on a Lie group. Hamiltonian reduction of free motion on a symmetric Riemann space with negative curvature leads to spin Calogero models. 3.Spin chains and lattice theories The energy current in the XX model and the aperiodic perturbation of couplings in the Heisenberg chain increase the entanglement entropy. The zero-entropy-density conjecture is sharp for translation-invariant states of spin chains. The continuum limit of the 4d Ising model is found to be trivial by MC methods but the convergence is very slow. 4. Quantum groupoids Depth 2 algebra extensions were characterized by bialgebroids, the analogues of Galois groups in the balanced case. The notion of Hopf algebroids was introduced. Their role was determined in cleft algebra extensions, in Hopf-Galois extensions, in non-commutative geometry

Comparative biocompatibility and antimicrobial studies of sorbic acid derivates

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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

Antiproliferative and Antimicrobial Activities of Selected Bryophytes

One-hundred and sixty-eight aqueous and organic extracts of 42 selected bryophyte species were screened in vitro for antiproliferative activity on a panel of human gynecological cancer cell lines containing HeLa (cervix epithelial adenocarcinoma), A2780 (ovarian carcinoma), and T47D (invasive ductal breast carcinoma) cells using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay and for antibacterial activity on 11 strains using the disc-diffusion method. A total of 99 extracts derived from 41 species exerted ≥25% inhibition of proliferation of at least one of the cancer cell lines at 10 μg/mL. In the cases of Brachythecium rutabulum, Encalypta streptocarpa, Climacium dendroides, Neckera besseri, Pleurozium schreberi, and Pseudoleskeella nervosa, more than one extract was active in the antiproliferative assay, whereas the highest activity was observed in the case of Paraleucobryum longifolium. From the tested families, Brachytheciaceae and Amblystegiaceae provided the highest number of antiproliferative extracts. Only 19 samples of 15 taxa showed moderate antibacterial activity, including the most active Plagiomnium cuspidatum, being active on 8 tested strains. Methicillin-resistant Staphylococcus aureus (MRSA) and Staphylococcus aureus were the most susceptible to the assayed species. This is the first report on the bioactivities of these 14 species

Protective Effect of Pure Sour Cherry Anthocyanin Extract on Cytokine-Induced Inflammatory Caco-2 Monolayers

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