On zero-divisors in group rings of groups with torsion

Nontrivial pairs of zero-divisors in group rings are introduced and discussed. A problem on the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of odd exponent $n \gg 1$ is solved in the affirmative. Nontrivial pairs of zero-divisors are also found in group rings of free products of groups with torsion.Comment: 8 pages, to appear in Canadian Math. Bul

On the Form Factors of the $D_{s}^{+}\to \phi\mu^{+}\nu_{\mu} decay

We apply the infinite mass effective theory, when a heavy quark mass tends to infinity, and Chiral perturbation theory at the quark level, based on the extended Nambu -- Jona -- Lasinio model with linear realization of chiral $U(3)\times U(3)$ symmetry, to calculate the form factors of the $D^{\,+}_{\,s}\to\phi~\mu^+~\nu_{\,\mu}$ decay up to the first order in current $s$ -- quark mass. The theoretical results are compared with experimental data and found to be in good agreement.Comment: 7pages, latex, no figure

Gauging N=4 supersymmetric mechanics II: (1,4,3) models from the (4,4,0) ones

Exploiting the gauging procedure developed by us in hep-th/0605211, we study the relationships between the models of N=4 mechanics based on the off-shell multiplets (4,4,0) and (1,4,3). We make use of the off-shell N=4, d=1 harmonic superspace approach as most adequate for treating this circle of problems. We show that the most general sigma-model type superfield action of the multiplet (1,4,3) can be obtained in a few non-equivalent ways from the (4,4,0) actions invariant under certain three-parameter symmetries, through gauging the latter by the appropriate non-propagating gauge multiplets. We discuss in detail the gauging of both the Pauli-Gursey SU(2) symmetry and the abelian three-generator shift symmetry. We reveal the (4,4,0) origin of the known mechanisms of generating potential terms for the multiplet (1,4,3), as well as of its superconformal properties. A new description of this multiplet in terms of unconstrained harmonic analytic gauge superfield is proposed. It suggests, in particular, a novel mechanism of generating the (1,4,3) potential terms via coupling to the fermionic off-shell N=4 multiplet (0,4,4).Comment: 27 page

Finite-Difference Calculations for Atoms and Diatomic Molecules in Strong Magnetic and Static Electric Fields

Fully numerical mesh solutions of 2D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of atoms and molecules in strong external fields where neither the external field nor the internal interactions can be considered as a perturbation. The applications of the present approach include calculations of atoms and diatomic molecules in strong static electric and magnetic fields. For the latter we have carried out Hartree-Fock calculations for He, Li, C and several other atoms. This yields in particular the first comprehensive investigation of the ground state configurations of the Li and C atoms in the whole range of magnetic fields (0<B<10000 a.u.) and a study of the ground state electronic configurations of all the atoms with 1<Z<11 and their ions A^+ in the high-field fully spin-polarised regime. The results in a case of a strong electric field relate to single-electron systems including the correct solution of the Schroedinger equation for the H_2^+ ion (energies and decay rates) and the hydrogen atom in strong parallel electric and magnetic fields.Comment: 20 pages, 7 figure

Strongly interacting σ\sigma-electrons and MgB2_2 superconductivity

MgB$(p^{n_{\sigma}}p^{n_{\pi}})_{2}$ is classified as a system with strongly interacting $\sigma$-electrons and non-correlated $\pi$-electrons of boron ions. The kinematic and Coulomb interaction V between the orbitally degenerated $\sigma$-electrons provide the superconducting state with an anisotropic gap of s*-wave symmetry. The critical temperature $T_c$ has a non-monotonic dependence on the distance r between the centers of gravity of $\sigma$- and $\pi$-bands. MgB$_2$ corresponds to r=0.085 eV and V=0.45 eV in our model with flat bands. The derived superconducting density of electronic states is in good agreement with available experimental and theoretical data. The possibilities for increasing $T_c$ are discussed.Comment: 8 pages, 4 figure

On kaonic deuterium. Quantum field theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K^-d state A_(K d). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a smooth elastic background, and the inelastic channels K^- d -> NY and K^- d -> NY pion, with Y = Sigma^(+/-), Sigma^0 and Lambda^0, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_(Kd) -> NY and experimental data on the rates of the NY-pair production in the reactions K^-d -> NY. We obtain Gamma_{1s} = (630 +/-100) eV. For the shift of the energy level of the ground state of kaonic deuterium we predict epsilon_(1s) = (353 +/-60)eV.Comment: 73 pages,10 figures, Latex, We have slightly corrected the contribution of the double scattering. The change of the S-wave scattering length of K^-d scattering does not go beyond the theoretical uncertainty, which is about 18

Universal Superfield Action for N=8→N=4N=8 \to N=4 Partial Breaking of Global Supersymmetry in D=1

We explicitly construct N=4 worldline supersymmetric minimal off-shell actions for five options of 1/2 partial spontaneous breaking of $N=8, d=1$ Poincar\'e supersymmetry. We demonstrate that the action for the N=4 Goldstone supermultiplet with four fermions and four auxiliary components is a universal one. The remaining actions for the Goldstone supermultiplets with physical bosons are obtained from the universal one by off-shell duality transformations.Comment: 9 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-

Two-dimensional negative donors in magnetic fields

A finite-difference solution of the Schroedinger equation for negative donor centers D^- in two dimensions is presented. Our approach is of exact nature and allows us to resolve a discrepancy in the literature on the ground state of a negative donor. Detailed calculations of the energies for a number of states show that for field strengths less than \gamma=0.117 a.u. the donor possesses one bound state, for 0.117<\gamma<1.68 a.u. there exist two bound states and for field strengths \gamma>1.68 a.u. the system possesses three bound states. Further relevant characteristics of negative donors in magnetic fields are provided.Comment: 7 pages, 1 figur