Star product formula of theta functions

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.Comment: 12 page

Pressure-induced metal-insulator transition in MgV_2O_4

On the basis of experimental thermoelectric power results and ab initio calculations, we propose that a metal-insulator transition takes place at high pressure (approximately 6 GPa) in MgV_2O_4.Comment: 2 pages, 3 figures, accepted in Physica B (Strongly Correlated Electron Systems '07

A supergeometric approach to Poisson reduction

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to describe the corresponding reductions.Comment: 40 pages. Final version accepted for publicatio

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-$\gamma$-unstable and, vibrational-$\gamma$-unstable transitions) are reanalyzed. A new kind of plot is presented for studying phase transitions in finite systems such as atomic nuclei. The importance of analyzing binding energies and not only energy spectra and electromagnetic transitions, describing transitional regions is emphasized. We finally discuss a number of realistic examples.Comment: 34 pages, TeX (ReVTeX). 12 ps figures. 3 tables. Submitted to Nucl. Phys.

Can the magnetic moment contribution explain the A_y puzzle?

We evaluate the full one-photon-exchange Born amplitude for $Nd$ scattering. We include the contributions due to the magnetic moment of the proton or neutron, and the magnetic moment and quadrupole moment of the deuteron. It is found that the inclusion of the magnetic-moment interaction in the theoretical description of the $Nd$ scattering observables cannot resolve the long-standing $A_y$ puzzle.Comment: 7 pages, 2 Postscript figures; to appear in Phys.Rev.

Improved Estimates of Cosmological Perturbations

We recently derived exact solutions for the scalar, vector and tensor mode functions of a single, minimally coupled scalar plus gravity in an arbitrary homogeneous and isotropic background. These solutions are applied to obtain improved estimates for the primordial scalar and tensor power spectra of anisotropies in the cosmic microwave background.Comment: 31 pages, 4 figures, LaTeX 2epsilon, this version corrects an embarrasing mistake (in the published version) for the parameter q_C. Affected eqns are 105, 109-110, 124, 148-153 and 155-15

An Overview of the 13:8 Mean Motion Resonance between Venus and Earth

It is known since the seminal study of Laskar (1989) that the inner planetary system is chaotic with respect to its orbits and even escapes are not impossible, although in time scales of billions of years. The aim of this investigation is to locate the orbits of Venus and Earth in phase space, respectively to see how close their orbits are to chaotic motion which would lead to unstable orbits for the inner planets on much shorter time scales. Therefore we did numerical experiments in different dynamical models with different initial conditions -- on one hand the couple Venus-Earth was set close to different mean motion resonances (MMR), and on the other hand Venus' orbital eccentricity (or inclination) was set to values as large as e = 0.36 (i = 40deg). The couple Venus-Earth is almost exactly in the 13:8 mean motion resonance. The stronger acting 8:5 MMR inside, and the 5:3 MMR outside the 13:8 resonance are within a small shift in the Earth's semimajor axis (only 1.5 percent). Especially Mercury is strongly affected by relatively small changes in eccentricity and/or inclination of Venus in these resonances. Even escapes for the innermost planet are possible which may happen quite rapidly.Comment: 14 pages, 11 figures, submitted to CMD

Inflation with a constant ratio of scalar and tensor perturbation amplitudes

The single scalar field inflationary models that lead to scalar and tensor perturbation spectra with amplitudes varying in direct proportion to one another are reconstructed by solving the Stewart-Lyth inverse problem to next-to-leading order in the slow-roll approximation. The potentials asymptote at high energies to an exponential form, corresponding to power law inflation, but diverge from this model at low energies, indicating that power law inflation is a repellor in this case. This feature implies that a fine-tuning of initial conditions is required if such models are to reproduce the observations. The required initial conditions might be set through the eternal inflation mechanism. If this is the case, it will imply that the spectral indices must be nearly constant, making the underlying model observationally indistinguishable from power law inflation.Comment: 20 pages, 7 figures. Major changes to the Introduction following referee's comments. One figure added. Some other minor changes. No conclusion was modifie

QED and String Theory

We analyze the D9-D9bar system in type IIB string theory using Dp-brane probes. It is shown that the world-volume theory of the probe Dp-brane contains two-dimensional and four-dimensional QED in the cases with p=1 and p=3, respectively, and some applications of the realization of these well-studied quantum field theories are discussed. In particular, the two-dimensional QED (the Schwinger model) is known to be a solvable theory and we can apply the powerful field theoretical techniques, such as bosonization, to study the D-brane dynamics. The tachyon field created by the D9-D9bar strings appears as the fermion mass term in the Schwinger model and the tachyon condensation is analyzed by using the bosonized description. In the T-dualized picture, we obtain the potential between a D0-brane and a D8-D8bar pair using the Schwinger model and we observe that it consists of the energy carried by fundamental strings created by the Hanany-Witten effect and the vacuum energy due to a cylinder diagram. The D0-brane is treated quantum mechanically as a particle trapped in the potential, which turns out to be a system of a harmonic oscillator. As another application, we obtain a matrix theory description of QED using Taylor's T-duality prescription, which is actually applicable to a wide variety of field theories including the realistic QCD. We show that the lattice gauge theory is naturally obtained by regularizing the matrix size to be finite.Comment: 33 pages, Latex, 4 figures, a reference adde