Deformation Quantization in Singular Spaces

We present a method of quantizing analytic spaces $X$ immersed in an arbitrary smooth ambient manifold $M$. Remarkably our approach can be applied to singular spaces. We begin by quantizing the cotangent bundle of the manifold $M$. Using a super-manifold framework we modify the Fedosov construction in a way such that the $\star$-product of the functions lifted from the base manifold turns out to be the usual commutative product of smooth functions on $M$. This condition allows us to lift the ideals associated to the analytic spaces on the base manifold to form left (or right) ideals on (\mc{O}_{\Omega^1 M}[[\hbar]],\starl) in a way independent of the choice of generators and leading to a finite set of PDEs defining the functions in the quantum algebra associated to $X$. Some examples are included.Comment: 14 page

Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces

Finsler and Lagrange spaces can be equivalently represented as almost Kahler manifolds enabled with a metric compatible canonical distinguished connection structure generalizing the Levi Civita connection. The goal of this paper is to perform a natural Fedosov-type deformation quantization of such geometries. All constructions are canonically derived for regular Lagrangians and/or fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23 page

BRST quantization of quasi-symplectic manifolds and beyond

We consider a class of \textit{factorizable} Poisson brackets which includes almost all reasonable Poisson structures. A particular case of the factorizable brackets are those associated with symplectic Lie algebroids. The BRST theory is applied to describe the geometry underlying these brackets as well as to develop a deformation quantization procedure in this particular case. This can be viewed as an extension of the Fedosov deformation quantization to a wide class of \textit{irregular} Poisson structures. In a more general case, the factorizable Poisson brackets are shown to be closely connected with the notion of $n$-algebroid. A simple description is suggested for the geometry underlying the factorizable Poisson brackets basing on construction of an odd Poisson algebra bundle equipped with an abelian connection. It is shown that the zero-curvature condition for this connection generates all the structure relations for the $n$-algebroid as well as a generalization of the Yang-Baxter equation for the symplectic structure.Comment: Journal version, references and comments added, style improve

ЕФЕКТИ ПОДАТКОВИХ ТРАНСФОРМАЦІЙ

The tax reforms in Ukraine last a long time but do not lead to the desirable results. It actualizes the research of mistakes and wrong managerial decisions. The authors consider that the main reason of ineffective tax reforms is ignoring the objective features of taxes and fundamentals of management under policy making. The article aims to prove this hypothesis. The authors use the method of logical assumptions based on the interrelation of objective and subjective as well as the statistical data analysis for evidence. They show that the definition of taxes can be interpreted in different way. It predetermines the tax reform beneficiary: government or society. The Ukrainian government determines the tax reform purposes in abstractive form without quantitative indicators and does not analyses the previous tax transformations results. Such management does not meet the principles that objectively predetermine tax reform successful results. The tax transformations during 2014—2018 led to the tax burden grows. In the result the government revenue increased. At the same time it led to the cutback of consumption demand. The indicators of the pharmacy market and excise goods market development prove this conclusion. Such effect was a logical result of the ignoring objective properties of taxes. Managerial decisions on the tax system reforming contradicted to the purpose of the tax system reform in Ukraine — to provide economic grows. The statistical data demonstrate a little GDP grows. But most of people became much poor through unequal distribution of income. The Ukrainian government did not use the natural properties of tax as regulators of consumption demand through shifting the tax burden from poor sector of population due to towards the income that significantly exceeds the average. The authors suggest the further ways of the tax system reforming in Ukraine.Налоговые реформы в Украине не приводят к желаемым результатам. Считаем, что основной причиной является игнорирование объективных особенностей налогов и основ менеджмента при разработке и реализации налоговой политики. Цель статьи — доказать эту гипотезу. Доказано, что управленческие решения по реформированию налоговой системы противоречат цели реформирования налоговой системы в Украине — обеспечить экономический рост.Податкові реформи в Україні змінюють одна одну, проте не призводить до бажаних результатів. Такий стан речей актуалізує дослідження помилок і неправильних управлінських рішень, які ухвалюють під час реформування. Вважаємо, що головною причиною неефективних податкових реформ є ігнорування об’єктивних особливостей податків та основ менеджменту під час розроблення та реалізації податкової політики. Мета статті — довести цю гіпотезу. У процесі дослідження застосовуємо метод логічних умовиводів на основі взаємозв’язку об’єктивного і суб’єктивного та статистичний аналіз даних. Вони показують, що визначення податків можна трактувати по-різному. Це активізує бенефіціара податкової реформи: уряд чи суспільство. Уряд України визначає цілі податкової реформи в абстрактній формі без кількісних показників і не аналізує результати попередніх податкових трансформацій. Такий підхід не відповідає засадам управління. Податкові трансформації протягом 2014—2018 років призвели до зростання податкового навантаження. У результаті доходи держави зросли. Водночас це призвело до скорочення споживчого попиту. Такий висновок підтверджують показники розвитку фармацевтичного ринку і ринку підакцизних товарів. Ефект був логічним результатом ігнорування об’єктивних властивостей податків. Управлінські рішення щодо реформування податкової системи суперечать меті реформування податкової системи в Україні — забезпечити економічне зростання. Статистичні дані свідчать про незначне зростання ВВП. Але більшість людей стали значно біднішими через нерівномірний розподіл доходів. Український уряд не використовував природні властивості податків як регуляторів споживчого попиту через перенесення податкового тягаря з бідних верств населення на платників, дохід яких значно перевищує середній. Пропонуємо подальші напрями податкових трансформацій

Higher order relations in Fedosov supermanifolds

Higher order relations existing in normal coordinates between affine extensions of the curvature tensor and basic objects for any Fedosov supermanifolds are derived. Representation of these relations in general coordinates is discussed.Comment: 11 LaTex pages, no figure

Scalar Casimir Energies of Tetrahedra

New results for scalar Casimir self-energies arising from interior modes are presented for the three integrable tetrahedral cavities. Since the eigenmodes are all known, the energies can be directly evaluated by mode summation, with a point-splitting regulator, which amounts to evaluation of the cylinder kernel. The correct Weyl divergences, depending on the volume, surface area, and the corners, are obtained, which is strong evidence that the counting of modes is correct. Because there is no curvature, the finite part of the quantum energy may be unambiguously extracted. Dirichlet and Neumann boundary conditions are considered and systematic behavior of the energy in terms of geometric invariants is explored.Comment: Talk given at QFEXT 1

Surface potential at a ferroelectric grain due to asymmetric screening of depolarization fields

Nonlinear screening of electric depolarization fields, generated by a stripe domain structure in a ferroelectric grain of a polycrystalline material, is studied within a semiconductor model of ferroelectrics. It is shown that the maximum strength of local depolarization fields is rather determined by the electronic band gap than by the spontaneous polarization magnitude. Furthermore, field screening due to electronic band bending and due to presence of intrinsic defects leads to asymmetric space charge regions near the grain boundary, which produce an effective dipole layer at the surface of the grain. This results in the formation of a potential difference between the grain surface and its interior of the order of 1 V, which can be of either sign depending on defect transition levels and concentrations. Exemplary acceptor doping of BaTiO3 is shown to allow tuning of the said surface potential in the region between 0.1 and 1.3 V.Comment: 14 pages, 11 figures, submitted to J. Appl. Phy

Stiffness of RBC optical confinement affected by optical clearing

In vivo optical trapping is a novel applied direction of an optical manipulation, which enables one to noninvasive measurement of mechanical properties of cells and tissues in living animals directly. But an application area of this direction is limited because strong scattering of many biological tissues. An optical clearing enables one to decrease the scattering and therefore increase a depth of light penetration, decrease a distortion of light beam, improve a resolution in imaging applications. Now novel methods had appeared for a measurement an optical clearing degree at a cellular level. But these methods aren’t applicable in vivo. In this paper we present novel measurement method of estimate of the optical clearing, which are based on a measurement of optical trap stiffness. Our method may be applicable in vivo

Symplectic geometries on supermanifolds

Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of symplectic geometries on supermanifolds.Comment: LaTex, 1o pages, LaTex, changed conten

Direct Detection of Electroweak-Interacting Dark Matter

Assuming that the lightest neutral component in an SU(2)L gauge multiplet is the main ingredient of dark matter in the universe, we calculate the elastic scattering cross section of the dark matter with nucleon, which is an important quantity for the direct detection experiments. When the dark matter is a real scalar or a Majorana fermion which has only electroweak gauge interactions, the scattering with quarks and gluon are induced through one- and two-loop quantum processes, respectively, and both of them give rise to comparable contributions to the elastic scattering cross section. We evaluate all of the contributions at the leading order and find that there is an accidental cancellation among them. As a result, the spin-independent cross section is found to be O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio