De Sitter Invariant Vacuum States, Vertex Operators, and Conformal Field Theory Correlators

We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group $SO(1,d)$ and supply its physical interpretation in terms of the Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike infinities on de Sitter space reproduce correlation functions in $(d-1)$-dimensional Euclidean conformal field theory (CFT) on $S^{d-1}$ for scalar operators with arbitrary real conformal dimensions. We also compute correlation functions for a vertex operator $e^{i\hat{S}(u)}$ on the \L obaczewski space and find that they also reproduce correlation functions of the same CFT. The massless field $\hat{S}(u)$ is the nonlocal transform of the massless field $\hat{S}(x)$ on de Sitter space introduced by one of us.Comment: 14 pages, LaTeX file We thank Roman Jackiw for bringing to our attention Ref. 1

On Pairs of Difference Operators Satisfying: [P,Q] = Id

Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$ to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The first class, generalizing the central difference scheme, is shown to give unitary equivalent representations. For the second case we construct a large class of examples, generalizing previously known difference operator realizations of $[P,X]=Id$.Comment: 32 pages, plain Te

Edukacja regionalna i patriotyczna w warunkach wielokulturowości

Edukacja w Polsce jest mocno zakorzeniona w wielokulturowości, regionalizmie i tradycji patriotycznej. Była i jest zorientowana okcydentalistycznie. Dawniej pojęcia te kojarzono ze wzniosłością i wielkimi sprawami narodu i państwa. W dobie demokratyzacji, modernizacji, integracji i globalizacji nabierają one nowego znaczenia. Zaczynają absorbować różnorodne pierwiastki życia codziennego. Powinny się zatem doczekać reaktualizacji i głębszego umocowania w teorii dydaktycznej. Jest to niezbędne szkole, która programowo realizuje edukacje (ścieżki edukacyjne): regionalną, kulturową i europejską. Autorzy koncentrują się na refleksji teoretycznej. Nie omawiają rozwiązań metodycznych, które jej towarzyszą

Hesperidin Displays Relevant Role in the Nutrigenomic Effect of Orange Juice on Blood Leukocytes in Human Volunteers: A Randomized Controlled Cross-Over Study

We previously showed, in healthy, middle-aged, moderately overweight men, that orange juice decreases diastolic blood pressure and significantly improves postprandial microvascular endothelial reactivity and that hesperidin could be causally linked to the observed beneficial effect of orange juice. The objective was to determine the effect of chronic consumption of orange juice on the gene expression profile of leukocytes in healthy volunteers and to assess to what extent hesperidin is involved in the effect of orange juice.Volunteers were included in a randomized, controlled, crossover study. Throughout three 4-week periods, volunteers consumed daily: 500 ml orange juice, 500 ml control drink plus hesperidin or 500 ml control drink and placebo. Blood samplings were performed on 10 overnight-fasted subjects after the 4-week treatment period. Global gene expression profiles were determined using human whole genome cDNA microarrays. Both orange juice and hesperidin consumption significantly affected leukocyte gene expression. Orange juice consumption induced changes in expression of, 3,422 genes, while hesperidin intake modulated the expression of 1,819 genes. Between the orange juice and hesperidin consumption groups, 1,582 regulated genes were in common. Many of these genes are implicated in chemotaxis, adhesion, infiltration and lipid transport, which is suggestive of lower recruitment and infiltration of circulating cells to vascular wall and lower lipid accumulation.This study shows that regular consumption of orange juice for 4 weeks alters leukocyte gene expression to an anti-inflammatory and anti-atherogenic profile, and hesperidin displays a relevant role in the genomic effect of this beverage.ClinicalTrials.gov NCT 00983086