Global Symmetries of Noncommutative Space-time

The global counterpart of infinitesimal symmetries of noncommutative space-time is discussed.Comment: 7 pages, no figures; minor changes in the bibliography; final version accepted for publication in Phys. Rev.

A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page

A Note on the Cosmological Dynamics in Finite-Range Gravity

In this note we consider the homogeneous and isotropic cosmology in the finite-range gravity theory recently proposed by Babak and Grishchuk. In this scenario the universe undergoes late time accelerated expansion if both the massive gravitons present in the model are tachyons. We carry out the phase space analysis of the system and show that the late-time acceleration is an attractor of the model.Comment: RevTex, 4 pages, two figures, New references added, To appear in IJMP

A procedure for evaluation of the effect of water injection into a reservoir on oil production on example of Tournaisian deposits of the Sosnovskoe gas-oil field

The effect of water injection into a reservoir on oil production for Tournaisian deposits of the Sosnovskoe gas-oil field is evaluated. Statistical methods such as correlation, regression and stepwise discriminant analysis were used. Data on monthly and cumulative oil production, on amount of water injected into the reservoir from four injection and twelve production wells was used. Based on the data, studies have been performed to assess the effect of the volume of monthly water injection into the reservoir on monthly oil production, provided that each injection well affects only nearby producing wells. It was explained why there was no correlation between the parameters of monthly injection and monthly oil production. Then, in order to evaluate the efficiency of water injection into the reservoir, it was decided to use the data from the accumulated volume of water injection and the accumulated volume of oil production. It was found that there is a relationship between the parameters of the accumulated volume of water injection and the accumulated volume of oil production. The greater the accumulated volume of water injection, the greater the accumulated volume of oil production, but the gradients of increase for all wells are individual. Three areas were defined on the graphs. Relationships between the parameters have a high degree of linearity over a certain range. In order to establish the boundaries of those areas where the influence of the values of the accumulated volume of water injection on the accumulated volume of oil production is conditionally homogeneous, linear discriminant analysis was used. Results of the evaluation study show that water injection into the reservoir has a different degree of influence on the production wells. This analysis can be further applied to substantiate workovers and to identify hydrodynamic communication

Basic Types of Legal Aid in Criminal Legal Proceedings

The study of the features of legal assistance in the criminal process as a comprehensive legislative and scientific category allowed the Author to determine the classification grounds and distinguish four of its main types: legal assistance provided by state criminal justice bodies and their officials; qualified legal assistance provided by lawyers and legal advisers; legal assistance provided by close relatives or other persons who are participants in the criminal process; legal assistance provided by authorized persons who are not subjects of criminal proceedings

Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion

It is well known that the long-range nature of the Coulomb interaction makes the definition of asymptotic ``in'' and ``out'' states of charged particles problematic in quantum field theory. In particular, the notion of a simple particle pole in the vacuum charged particle propagator is untenable and should be replaced by a more complicated branch cut structure describing an electron interacting with a possibly infinite number of soft photons. Previous work suggests a Dirac propagator raised to a fractional power dependent upon the fine structure constant, however the exponent has not been calculated in a unique gauge invariant manner. It has even been suggested that the fractal ``anomalous dimension'' can be removed by a gauge transformation. Here, a gauge invariant non-perturbative calculation will be discussed yielding an unambiguous fractional exponent. The closely analogous case of soft graviton exponents is also briefly explored.Comment: Updated with a corrected sign error, longer discussion of fractal dimension, and more reference

Exotic Statistics for Ordinary Particles in Quantum Gravity

Objects exhibiting statistics other than the familiar Bose and Fermi ones are natural in theories with topologically nontrivial objects including geons, strings, and black holes. It is argued here from several viewpoints that the statistics of ordinary particles with which we are already familiar are likely to be modified due to quantum gravity effects. In particular, such modifications are argued to be present in loop quantum gravity and in any theory which represents spacetime in a fundamentally piecewise-linear fashion. The appearance of unusual statistics may be a generic feature (such as the deformed position-momentum uncertainty relations and the appearance of a fundamental length scale) which are to be expected in any theory of quantum gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation Essay Competitio

Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries

The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$ a three parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged center of the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a three-dimensional complex hypersurface which remains invariant under the action of an infinite-dimensional group of analytic transformations, called the quantum coadjoint action.Comment: 52 pages, TCI LaTex, v2: equation (167) corrected, two references adde

Low Momentum Scattering in the Dirac Equation

It is shown that the amplitude for reflection of a Dirac particle with arbitrarily low momentum incident on a potential of finite range is -1 and hence the transmission coefficient T=0 in general. If however the potential supports a half-bound state at k=0 this result does not hold. In the case of an asymmetric potential the transmission coefficient T will be non-zero whilst for a symmetric potential T=1.Comment: 12 pages; revised to include additional references; to be published in J Phys