The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background

We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.Comment: 41 pages, uses LaTeX 2e, version 2 has some typoes correcte

Theory of gravitation theories: a no-progress report

Already in the 1970s there where attempts to present a set of ground rules, sometimes referred to as a theory of gravitation theories, which theories of gravity should satisfy in order to be considered viable in principle and, therefore, interesting enough to deserve further investigation. From this perspective, an alternative title of the present paper could be ``why are we still unable to write a guide on how to propose viable alternatives to general relativity?''. Attempting to answer this question, it is argued here that earlier efforts to turn qualitative statements, such as the Einstein Equivalence Principle, into quantitative ones, such as the metric postulates, stand on rather shaky grounds -- probably contrary to popular belief -- as they appear to depend strongly on particular representations of the theory. This includes ambiguities in the identification of matter and gravitational fields, dependence of frequently used definitions, such as those of the stress-energy tensor or classical vacuum, on the choice of variables, etc. Various examples are discussed and possible approaches to this problem are pointed out. In the course of this study, several common misconceptions related to the various forms of the Equivalence Principle, the use of conformal frames and equivalence between theories are clarified.Comment: Invited paper in the Gravity Research Foundation 2007 special issue to be published by Int. J. Mod. Phys.

МЕТОД РАСЧЕТА ПЕРЕХОДНЫХ РЕЖИМОВ ГРЕБНЫХ ЭЛЕКТРОЭНЕРГЕТИЧЕСКИХ УСТАНОВОК ЭЛЕКТРОХОДОВ

The purpose of the work is to develop the method for calculating the transient modes of electric ships’ propelling electric plants during maneuver. This will allow us to evaluate and improve the maneuverability of vessels with electric motion. Methodology. The solution to the problems is proposed to be carried out on the basis of mathematical modeling of maneuvering modes. The duration of transient modes in an electric power plant at electric ships’ maneuvers is commensurable with the transient operation modes of the vessel itself. Therefore, the analysis of the electric power plants’ maneuvering modes should be made in unity with all the components of the ship’s propulsion complex. Results. A specified mathematical model of transient regimes of electric ship’s propulsion complex, including thermal motors, synchronous generators, electric power converters, propulsion motors, propellers, rudder, ship’s hull is developed. The model is universal. It covers the vast majority of modern and promising electric ships with a traditional type of propulsors. It allows calculating the current values of the basic mode indicators and assessing the quality indicators of maneuvering. The model is made in relative units. Dimensionless parameters of the complex are obtained. These parameters influence the main indicators of the quality of maneuvering. The adequacy of the suggested specified mathematical model and the developed computation method based on it were confirmed. To do this, the results of mathematical modeling for a real electric ship were compared with the data obtained in the course of field experiments conducted by other researchers. Originality. The mathematical description of a generator unit, as an integral part of an indivisible ship’s propulsion complex, makes it possible to calculate the dynamic operation modes of electric power sources during electric vessels’ maneuvering. There is an opportunity to design the electric ships’ propulsion power plant according to the final result – according to the indicators characterizing the vessel and its maneuvering properties. The use of a system of dimensionless units provides a generality to the results obtained. Electric ships with equal values of dimensionless parameters will have correspondingly the same values (in relative units) of maneuvering quality indicators. Practical value. The developed mathematical model and the research method constructed on its basis allow calculating the current values of the basic regime parameters of all the components of the ship’s propulsion complex. A mathematical apparatus for estimating the main indicators of the quality of electric ships’ maneuvering is proposed. There is an opportunity to improve the electric ships’ maneuvering characteristics by optimizing the operation of propulsion motors.Целью работы является разработка метода расчета переходных режимов гребных электроэнергетических установок в составе судовых пропульсивных комплексов. Методика. На маневрах продолжительности переходных режимов в электроэнергетической установке соизмеримы с переходными режимами работы судна. Поэтому анализ маневренных режимов ее работы следует проводить в единстве со всеми составными частями судового пропульсивного комплекса.            Результаты. Разработаны уточненная математическая модель и метод расчета переходных режимов всех составных частей пропульсивного комплекса электрохода на маневрах. Найдены безразмерные параметры комплекса. Они определяют основные показатели качества маневрирования. Адекватность модели и метода расчета подтверждены сравнением результатов математического моделирования с натурными экспериментами. Научная новизна. Метод расчета позволяет рассчитывать динамические режимы работы всех составных частей комплекса. Появляется возможность проектирования гребных электроэнергетических установок по конечному результату – по показателям качества маневрирования судна. Практическое значение. Метод расчета позволяет проводить исследования поведения пропульсивных комплексов на маневрах и отыскивать пути повышения маневренности электроходов

Extended Quintessence with non-minimally coupled phantom scalar field

We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion that which cosmological scenario is realized depends on behavior of the system on the phase plane $(\psi, \psi')$. We formulate simple conditions on the value of coupling constant $\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value $w=-1$. We describe this condition in terms of slow-roll parameters calculated at the critical point. We discover that the generic trajectories in the focus-attractor scenario come from the unstable node. It is also investigated the exact form of the parametrization of the equation of state parameter $w(z)$ (directly determined from dynamics) which assumes a different form for both scenarios.Comment: revtex4, 15 pages, 9 figures; (v2) published versio

Two loop stress-energy tensor for inflationary scalar electrodynamics

We calculate the expectation value of the coincident product of two field strength tensors at two loop order in scalar electrodynamics on de Sitter background. The result agrees with the stochastic formulation which we have developed in a companion paper [2] for the nonperturbative resummation of leading logarithms of the scale factor. When combined with a previous computation of scalar bilinears [1], our current result also gives the two loop stress-energy tensor for inflationary scalar electrodynamics. This shows a secular decrease in the vacuum energy which derives from the vacuum polarization induced by the inflationary production of charged scalars.Comment: 62 pages, 1 eps figur

Manifestation of the Arnol'd Diffusion in Quantum Systems

We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled non-linear oscillators one of which is governed by an external periodic force with two frequencies. In the classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance, and leads to an increase of total energy of the system. We show that the quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics, and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.Comment: RevTex, 4 pages including 7 ps-figures, corrected forma

"Massless" vector field in de Sitter Universe

In the present work the massless vector field in the de Sitter (dS) space has been quantized. "Massless" is used here by reference to conformal invariance and propagation on the dS light-cone whereas "massive" refers to those dS fields which contract at zero curvature unambiguously to massive fields in Minkowski space. Due to the gauge invariance of the massless vector field, its covariant quantization requires an indecomposable representation of the de Sitter group and an indefinite metric quantization. We will work with a specific gauge fixing which leads to the simplest one among all possible related Gupta-Bleuler structures. The field operator will be defined with the help of coordinate independent de Sitter waves (the modes) which are simple to manipulate and most adapted to group theoretical matters. The physical states characterized by the divergencelessness condition will for instance be easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemanian manifold for the modes and the two-point function.Comment: 33 pages, 3 figure

Conformally invariant wave-equations and massless fields in de Sitter spacetime

Conformally invariant wave equations in de Sitter space, for scalar and vector fields, are introduced in the present paper. Solutions of their wave equations and the related two-point functions, in the ambient space notation, have been calculated. The ``Hilbert'' space structure and the field operator, in terms of coordinate independent de Sitter plane waves, have been defined. The construction of the paper is based on the analyticity in the complexified pseudo-Riemanian manifold, presented first by Bros et al.. Minkowskian limits of these functions are analyzed. The relation between the ambient space notation and the intrinsic coordinates is then studied in the final stage.Comment: 21 pages, LaTeX, some details adde

Renormalization of initial conditions and the trans-Planckian problem of inflation

Understanding how a field theory propagates the information contained in a given initial state is essential for quantifying the sensitivity of the cosmic microwave background to physics above the Hubble scale during inflation. Here we examine the renormalization of a scalar theory with nontrivial initial conditions in the simpler setting of flat space. The renormalization of the bulk theory proceeds exactly as for the standard vacuum state. However, the short distance features of the initial conditions can introduce new divergences which are confined to the surface on which the initial conditions are imposed. We show how the addition of boundary counterterms removes these divergences and induces a renormalization group flow in the space of initial conditions.Comment: 22 pages, 4 eps figures, uses RevTe

[Intra-population variation of genetic/oological parameters of Kharkiv population of black-headed gull] Внутpипопуляционная изменчивость генетико-оологических параметров харьковской популяции озерной чайки

Чеpников В.Ф., Романов М.H., Кутнюк П.И. Для оценки непрерывной и дискретной внутрипопуляционной изменчивости по признакам длины (EL), ширины (EW), индекса формы (ESI), величины асимметрии (AU), массы яиц (EM) и оптической плотности фона скорлупы (ESBOD) использовали оологический материал, собранный в двух колониях озерной чайки (Larus ridibundus L.) — змиевской (n = 94) и чугуевской (n = 47). Достоверных различий по этим признакам между двумя колониями не обнаружено: средняя значения признаков составили соответственно 52,4 0,17 мм; 37,0 0,09 мм; 0,707±0,002; 22,1±0,07 мм; 37,3±0,23 г; 84,1±1,11 сБ; коэффициент вариации — 3,82; 2,76; 3,90; 3,71; 7,24 и 15,70% соответственно. Частоты аллелей по аутосомному полиморфному локусу овоглобулина G3 составили в змиевской субпопуляции: G3A — 0,567±0,063, G3B — 0,433±0,063; в чугуевской субпопуляции: G3A — 0,543±0,084, G3B — 0,457±0,084. В змиевской субпопуляции отмечен также полиморфизм по аутосомному локусу овальбумина (частоты OvA — 0,896±0,06; OvB — 0,104±0,062). Тест на равновесность распределения по Харди–Вайнбергу не выявил нарушения генетического равновесия по полиморфным луковом, детерминирующим синтез белков яиц в обеих субпопуляциях. Мера генетического сходства r для двух харьковских субпопуляций составила 0,973 (при критерии идентичности I = 4,7 и P > 0,05). В то же время найдены достоверные различия (P < 0,001) между двумя субпопуляциями по показателям внутрипопуляционного разнообразия: по среднему числу аллелей — 1,80±0,052 против 1,50±0,007 (при допустимом интервале 1–2) и доле редких аллелей — 0,001±0,026 против 0,012±0,005 (при допустимом интервале 0–1). В результате корреляционного анализа для яиц чаек харьковской популяции установлены достоверные связи между линейными показателями, между линейными и весовыми, между отдельными линейными и показателями интенсивности окраски фона скорлупы (таблица). В чугуевской субпопуляции наблюдали также достоверную корреляцию между массой яиц и оптической плотностью фона скорлупы (–0,415; P < 0,01)