Dynamical Abelian Projection of Gluodynamics

Assuming the monopole dominance, that has been proved in the lattice gluodynamics, to hold in the continuum limit, we develop an effective scalar field theory for QCD at large distances to describe confinement. The approach is based on a gauge (or projection) independent formulation of the monopole dominance and manifestly Lorentz invariant.Comment: A talk given at QCD96, Montpellier, France, July, 1996 (to appear in the Proceedings); plain Latex, 6 page

Gribov vs BRST

We investigate the way in which the Gribov problem is manifested in the BRST quantization of simple quantum mechanical models by comparing models with and without a Gribov problem. We show that the hermiticity and nilpotency of the BRST charge together with the Batalin-Vilkovisky theorem yield non-trivial supplementary conditions on gauge fixing fermions. If the gauge fixing fermion satisfies the supplementary conditions, the BRST physical states form a space isomorphic to the Dirac space, and the BRST formal path integral does not suffer from the Gribov problem. The conventional gauge fixing fermion, that gives rise to the Faddeev-Popov integral, fails to satisfy the supplementary conditions due to the Gribov problem. Alternatively, enforcing the conventional gauge fixing fermion, these supplementary conditions imply restrictions on the BRST physical states for which the Batalin-Vilkovisky theorem holds. We find that these BRST physical states are not isomorphic the Dirac states. This can be interpreted as a violation of the Batalin-Vilkovisky theorem on the space of Dirac states and implies a breakdown of unitarity and a general dependence of physical quantities on the gauge condition.Comment: 9 pages, Revtex, A better formulation of the conditions on the gauge fixing fermion is given, Several relevant references are added, To appear in Ann. Phys. (N.Y.

Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space

The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and the choice of the initial (before imposition of the constraints) ultralocal representation of the field operators is initially presented. As analogous examples demonstrate, the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical Hilbert space is developed and extensively analyzed.Comment: LaTeX, 42 pages, no figure

The ploidy and genetic structure of hybrid population of water frogs Pelophylax esculentus complex (Amphibia, Ranidae) of Ukraine fauna

The complex study, including allozyme variability and cytometry of hybrid populations of green frogs Pelophylax esculentus (L., 1758) complex has confirmed that the only region of Ukraine where allodip loid are encountered frequently is the Severski Donets basin (9% of all hybrids). In other areas, only two poly ploidy hybrids (0.9%) and one probably autopolyploid individual of each parental species have been regis tered. According to allozyme specters, all three polyploidy hybrids from the Severski Donets basin were males and belonged to biotype P. esculentus (=lessonae) – 2 ridibundus, and their population in this region has halved during the past decade

Inheritance of parental genomes by a hybrid form Rana “esculenta” (Amphibia, Ranidae)

In this study, quantitative analysis of paternal genome inheritance by a hybrid form Rana “esculenta” (= Rana esculenta L., 1758 × Rana ridibunda Pall., 1881) (Amphibia, Ranidae) was examined. The hybrid form examined was characterized by a polymodal mode of inheritance (genome of any of the parental species can be inherited). The absence of correlation between the proportion of normal gametes and either sex or ploidity of the producer was demonstrated. The gametes produced could be both haploid and diploid (hybrid or homozygous). The mechanism of alloploid reproduction is discussed

Wave packet propagation study of the charge transfer interaction in the F^- -Cu(111) and -Ag(111) systems

The electron transfer between an $F^{-}$ ion and $Cu(111)$ and $Ag(111)$ surfaces is studied by the wave packet propagation method in order to determine specifics of the charge transfer interaction between the negative ion and the metal surface due to the projected band gap. A new modeling of the $F^{-}$ ion is developed that allows one to take into account the six quasi-equivalent electrons of $F^{-}$ which are {\it a priori} active in the charge transfer process. The new model invokes methods of constrained quantum dynamics. The six-electron problem is transformed to two one-electron problems linked via a constraint. The projection method is used to develop a wave packet propagation subject to the modeling constraint. The characteristics (energy and width) of the ion $F^{-}$ ion level interacting with the two surfaces are determined and discussed in connection with the surface projected band gap.Comment: 34 pages, Revtex, 9 figures (postscript

The wave packet propagation using wavelets

It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The new method is compared with the fast Fourier algorithm. Depending on ratios of typical scales of a quantum system in question, the wavelet method appears to be faster by a few orders of magnitude.Comment: Latex 7 pages, 3 colored figures (Fig1 postscript, Fig2,3 gif) in files separate from the pape

Soliton solutions in an effective action for SU(2) Yang-Mills theory: including effects of higher-derivative term

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space upto fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the thoery contains an additional fourth-order term which destabilizes the soliton solution. In this paper, we derive the second derivative term perturbatively and show that the SFN model with the second derivative term possesses soliton solutions.Comment: 7 pages, 3 figure

An application of interpolating scaling functions to wave packet propagation

Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the underlying interpolating polynomial that is used to generate ISF. In this basis the potential energy matrix is diagonal and the kinetic energy matrix is sparse and, in the 1D case, has a band-diagonal structure. An important feature of the basis is that matrix elements of a Hamiltonian are exactly computed by means of simple algebraic transformations efficiently implemented numerically. Therefore the number of grid points and the order of the underlying interpolating polynomial can easily be varied allowing one to approach the accuracy of pseudospectral methods in a regular manner, similar to high order finite difference methods. The results of numerical simulations of an H+H_2 collinear collision show that the ISF provide one with an accurate and efficient representation for use in the wave packet propagation method.Comment: plain Latex, 11 pages, 4 figures attached in the JPEG forma

Gauge Orbit Types for Theories with Classical Compact Gauge Group

We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4. Complemented with earlier results on U(n) and SU(n) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way we derive the classification of principal bundles with structure group SO(n) over these manifolds and the Howe subgroups of SO(n).Comment: 57 page