Generalized Density Matrix Revisited: Microscopic Approach to Collective Dynamics in Soft Spherical Nuclei

The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field [Hartree-Fock-Bogoliubov (HFB) equation] and the harmonic potential [quasiparticle random phase approximation (QRPA)]. The method is applied to soft spherical nuclei, where the anharmonicities are essential for restoring the stability of the system, as the harmonic potential becomes small or negative. The approach is tested in three models of increasing complexity: the Lipkin model, model with factorizable forces, and the quadrupole plus pairing model.Comment: submitted to Physical Review C on 08 May, 201

SUq(2)SU_q(2) Lattice Gauge Theory

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters - the deformation parameter $\lambda$ and the lattice spacing $a$. We show that the system of Kogut and Susskind is recovered when $\lambda \rightarrow 0$, while QCD is recovered in the continuum limit (for any $\lambda$). We thus have the possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil

On the idempotents of Hecke algebras

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu--Markov trace of the idempotents.Comment: 11 page

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of "uniqueness" (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless $\phi^3$ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of Lipatov integrable chain model.Comment: 16 pages. To appear in "Physics of Atomic Nuclei" (Proceedings of SYMPHYS-XII, Yerevan, Armenia, July 03-08, 2006

Priority Development Projects of the Arctic Zone. Reconstruction of the Northern Sea Way

The article describes Arctic zone and the significance of its resources for the Russian Federation and foreign countries. The basic strategic documents of the Arctic zone are listed. Priority projects for the development of the Arctic zone are considered. The reference zones of development in the Arctic and the influence of their formation on the macro region are analyzed. Areas of the main projects implemented or planned for implementation in the Arctic zone of the Russian Federation in percentage terms are presented. The state program of the Russian Federation «Socio-economic development of the Arctic zone of the Russian Federation», stages of implementation are considered. The main events of the VII International Forum «The Arctic: the present and the future» are revealed. The characteristic of the Northern Sea Route is given, its social and economic efficiency for the Russian Federation and the regions of the North is justified. The Northern Sea Route and the Southern Sea Route are compared. The criteria for increasing the carrying capacity of the Northern Sea Route are given. Areas of funding for improving the infrastructure of the region are indicated. The problem directions of the Northern Sea Route development have been identified: financial support for Northern Sea Route rehabilitation projects, political confrontation and a lack of qualified personnel. The characteristic of professional standards and their benefits for the enterprises of the region is presented. Recommendations are given on involving people in production and in the region

Diffusion algebras

We define the notion of "diffusion algebras". They are quadratic Poincare-Birkhoff-Witt (PBW) algebras which are useful in order to find exact expressions for the probability distributions of stationary states appearing in one-dimensional stochastic processes with exclusion. One considers processes in which one has N species, the number of particles of each species being conserved. All diffusion algebras are obtained. The known examples already used in applications are special cases in our classification. To help the reader interested in physical problems, the cases N=3 and 4 are listed separately.Comment: 29 pages; minor misprints corrected, few references adde

Configuration interaction calculation of hyperfine and P,T-odd constants on ^{207}PbO excited states for the electron EDM experiments

We report first configuration interaction calculations of hyperfine constants A_\parallel and the effective electric field W_d acting on the electric dipole moment of the electron, in two excited electronic states of ^{207}PbO. The obtained hyperfine constants, A_\parallel = -3826 MHz for the a(1) state and A_\parallel = 4887 MHz for the B(1) state, are in very good agreement with the experimental data, -4113 MHz and 5000 \pm 200 MHz, respectively. We find W_d = -(6.1 ^{+1.8}_{-0.6}) 10^{24} Hz/(e cm) for a(1), and W_d = (8.0 \pm 1.6) 10^{24} Hz/(e cm) for B(1). The obtained values are analyzed and compared to recent relativistic coupled cluster results and a semiempirical estimate of W_d for the a(1) state.Comment: 6 pages, REVTeX4 style, submitted to Pthys.Rev.

A Twistor Formulation of the Non-Heterotic Superstring with Manifest Worldsheet Supersymmetry

We propose a new formulation of the $D=3$ type II superstring which is manifestly invariant under both target-space $N=2$ supersymmetry and worldsheet $N=(1,1)$ super reparametrizations. This gives rise to a set of twistor (commuting spinor) variables, which provide a solution to the two Virasoro constraints. The worldsheet supergravity fields are shown to play the r\^ole of auxiliary fields.Comment: 21p., LaTe

All bicovariant differential calculi on Glq(3,C) and SLq(3,C)

All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with the help of the R-matrix of GLq(3,C). Some calculi induce bicovariant differential calculi on SLq(3,C) and on real forms of GLq(3,C). For generic deformation parameter q there are six calculi on SLq(3,C), on SUq(3) there are only two. The classical limit q-->1 of bicovariant calculi on SLq(3,C) is not the ordinary calculus on SL(3,C). One obtains a deformation of it which involves the Cartan-Killing metric.Comment: 24 pages, LaTe

Covariant differential complexes on quantum linear groups

We consider the possible covariant external algebra structures for Cartan's 1-forms on GL_q(N) and SL_q(N). We base upon the following natural postulates: 1. the invariant 1-forms realize an adjoint representation of quantum group; 2. all monomials of these forms possess the unique ordering. For the obtained external algebras we define the exterior derivative possessing the usual nilpotence condition, and the generally deformed version of Leibniz rules. The status of the known examples of GL_q(N)-differential calculi in the proposed classification scheme, and the problems of SL_q(N)-reduction are discussed.Comment: 23 page