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

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

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

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

Preclinical study of the efficacy and safety of wound healing gel containing chitosan, taurine and allantoin

Objectives: To develop gel containing chitosan, taurine, allantoin, and to experimentally investigate its wound healing properties in preclinical studies on laboratory animal

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

Blood flow velocity measurements in chicken embryo vascular network via PIV approach

A method for measuring of blood velocity in the native vasculature of a chick embryo by the method of micro anemometry from particle images (μPIV) is improved. A method for interrogation regions sorting by the mask of the vasculature is proposed. A method for sorting of the velocity field of capillary blood flow is implemented. The in vitro method was evaluated for accuracy in a glass phantom of a blood vessel with a diameter of 50 μm and in vivo on the bloodstream of a chicken embryo, by comparing the transverse profile of the blood velocity obtained by the PIV method with the theoretical Poiseuille laminar flow profile

Cohomologies of the Poisson superalgebra

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket for arbitrary n>0. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys. supplemented by computation of the 3-rd trivial cohomolog

Traces for star products on the dual of a Lie algebra

In this paper, we describe all traces for the BCH star-product on the dual of a Lie algebra. First we show by an elementary argument that the BCH as well as the Kontsevich star-product are strongly closed if and only if the Lie algebra is unimodular. In a next step we show that the traces of the BCH star-product are given by the \ad-invariant functionals. Particular examples are the integration over coadjoint orbits. We show that for a compact Lie group and a regular orbit one can even achieve that this integration becomes a positive trace functional. In this case we explicitly describe the corresponding GNS representation. Finally we discuss how invariant deformations on a group can be used to induce deformations of spaces where the group acts on.Comment: 18 pages, LaTeX2e. Updated reference