A prototype for dS/CFT

We consider dS_2/CFT_1 where the asymptotic symmetry group of the de Sitter spacetime contains the Virasoro algebra. We construct representations of the Virasoro algebra realized in the Fock space of a massive scalar field in de Sitter, built as excitations of the Euclidean vacuum state. These representations are unitary, without highest weight, and have vanishing central charge. They provide a prototype for a new class of conformal field theories dual to de Sitter backgrounds in string theory. The mapping of operators in the CFT to bulk quantities is described in detail. We comment on the extension to dS_3/CFT_2.Comment: 17 pages, revtex

On compression of Bruhat-Tits buildings

We obtain an analog of the compression of angles theorem in symmetric spaces for Bruhat--Tits buildings of the type $A$. More precisely, consider a $p$-adic linear space $V$ and the set $Lat(V)$ of all lattices in $V$. The complex distance in $Lat(V)$ is a complete system of invariants of a pair of points of $Lat(V)$ under the action of the complete linear group. An element of a Nazarov semigroup is a lattice in the duplicated linear space $V\oplus V$. We investigate behavior of the complex distance under the action of the Nazarov semigroup on the set $Lat(V)$.Comment: 6 page

A Simple Analytic Solution for Tachyon Condensation

In this paper we present a new and simple analytic solution for tachyon condensation in open bosonic string field theory. Unlike the B_0 gauge solution, which requires a carefully regulated discrete sum of wedge states subtracted against a mysterious "phantom" counter term, this new solution involves a continuous integral of wedge states, and no regularization or phantom term is necessary. Moreover, we can evaluate the action and prove Sen's conjecture in a mere few lines of calculation.Comment: 44 pages

Segal-Bargmann-Fock modules of monogenic functions

In this paper we introduce the classical Segal-Bargmann transform starting from the basis of Hermite polynomials and extend it to Clifford algebra-valued functions. Then we apply the results to monogenic functions and prove that the Segal-Bargmann kernel corresponds to the kernel of the Fourier-Borel transform for monogenic functionals. This kernel is also the reproducing kernel for the monogenic Bargmann module.Comment: 11 page

Improvement of the patients management in spontaneous pneumothorax

The study presents analysis of treatment in 1329 patients with spontaneous pneumothorax (SP). In 385 patients VATS and videoassisted surgical procedures. Algorithm of clinical tactics based on the analysis of clinical variants of SP was elaborated. The algorithm of surgical treatment was also worked out depending on the nature of the picture revealed by VATS. The relapse rate in patients treated according to proposed algorithms appeared to be significantly (p< 0,01) lower compared with 38.9% in the group of patients where draining procedure were only applied.Проведен анализ лечения 1329 больных со спонтанным пневмотораксом (СП). У 385 пациентов выполнены видеоторакоскопические и видеоассистированные оперативные вмешательства. На основании анализа клинических вариантов СП разработан алгоритм лечебной тактики. Разработан алгоритм хирургической тактики в зависимости от характера картины, выявляемой при видеоторакоскопии. Доказаны преимущества лечения по предлагаемым алгоритмам: частота рецидивов СП здесь составила 3,6%, по сравнению с 38,9% в группе больных, где применялись только дренирующие процедуры

Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

On Deformations of n-Lie algebras

The aim of this paper is to review the deformation theory of $n$-Lie algebras. We summarize the 1-parameter formal deformation theory and provide a generalized approach using any unital commutative associative algebra as a deformation base. Moreover, we discuss degenerations and quantization of $n$-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other author

Introduction to representations of the canonical commutation and anticommutation relations

Lecture notes of a minicourse given at the Summer School on Large Coulomb Systems - QED in Nordfjordeid, 2003, devoted to representations of the CCR and CAR. Quasifree states, the Araki-Woods and Araki-Wyss representations, and the lattice of von Neumenn algebras in a bosonic/fermionic Fock space are discussed in detail