A new orthogonalization procedure with an extremal property

Various methods of constructing an orthonomal set out of a given set of linearly independent vectors are discussed. Particular attention is paid to the Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new orthogonalization procedure which, like the Schweinler- Wigner procedure, is democratic and is endowed with an extremal property is suggested.Comment: 7 pages, latex, no figures, To appear in J. Phys

Dynamical Symmetry Breaking in Planar QED

We investigate (2+1)-dimensional QED coupled with Dirac fermions both at zero and finite temperature. We discuss in details two-components (P-odd) and four-components (P-even) fermion fields. We focus on P-odd and P-even Dirac fermions in presence of an external constant magnetic field. In the spontaneous generation of the magnetic condensate survives even at infinite temperature. We also discuss the spontaneous generation of fermion mass in presence of an external magnetic field.Comment: 34 pages, 8 postscript figures, final version to appear on J. Phys.

Saari's homographic conjecture for planar equal-mass three-body problem in Newton gravity

Saari's homographic conjecture in N-body problem under the Newton gravity is the following; configurational measure \mu=\sqrt{I}U, which is the product of square root of the moment of inertia I=(\sum m_k)^{-1}\sum m_i m_j r_{ij}^2 and the potential function U=\sum m_i m_j/r_{ij}, is constant if and only if the motion is homographic. Where m_k represents mass of body k and r_{ij} represents distance between bodies i and j. We prove this conjecture for planar equal-mass three-body problem. In this work, we use three sets of shape variables. In the first step, we use \zeta=3q_3/(2(q_2-q_1)) where q_k \in \mathbb{C} represents position of body k. Using r_1=r_{23}/r_{12} and r_2=r_{31}/r_{12} in intermediate step, we finally use \mu itself and \rho=I^{3/2}/(r_{12}r_{23}r_{31}). The shape variables \mu and \rho make our proof simple

Ultra-High Energy Neutrino Fluxes: New Constraints and Implications

We apply new upper limits on neutrino fluxes and the diffuse extragalactic component of the GeV gamma-ray flux to various scenarios for ultra high energy cosmic rays and neutrinos. As a result we find that extra-galactic top-down sources can not contribute significantly to the observed flux of highest energy cosmic rays. The Z-burst mechanism where ultra-high energy neutrinos produce cosmic rays via interactions with relic neutrinos is practically ruled out if cosmological limits on neutrino mass and clustering apply.Comment: 10 revtex pages, 9 postscript figure

Position-dependent mass models and their nonlinear characterization

We consider the specific models of Zhu-Kroemer and BenDaniel-Duke in a sech$^{2}$-mass background and point out interesting correspondences with the stationary 1-soliton and 2-soliton solutions of the KdV equation in a supersymmetric framework.Comment: 8 Pages, Latex version, Two new references are added, To appear in J.Phys.A (Fast Track Communication

Enhanced electrical resistivity before N\'eel order in the metals, RCuAs2_2 (R= Sm, Gd, Tb and Dy

We report an unusual temperature (T) dependent electrical resistivity($\rho$) behavior in a class of ternary intermetallic compounds of the type RCuAs$_2$ (R= Rare-earths). For some rare-earths (Sm, Gd, Tb and Dy) with negligible 4f-hybridization, there is a pronounced minimum in $\rho$(T) far above respective N\'eel temperatures (T$_N$). However, for the rare-earths which are more prone to exhibit such a $\rho$(T) minimum due to 4f-covalent mixing and the Kondo effect, this minimum is depressed. These findings, difficult to explain within the hither-to-known concepts, present an interesting scenario in magnetism.Comment: Physical Review Letters (accepted for publication

An Effect of α′\alpha' Corrections on Racetrack Inflation

We study the effects of $\alpha '$ corrections to the K\"ahler potential on volume stabilisation and racetrack inflation. In a region where classical supergravity analysis is justified, stringy corrections can nevertheless be relevant for correctly analyzing moduli stabilisation and the onset of inflation.Comment: 13 pages, 4 figures. Typos corrected, references added, this version to appear in JHE

Duality for Exotic Bialgebras

In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.