N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -

We investigate particular models which can be N-fold supersymmetric at specific values of a parameter in the Hamiltonians. The models to be investigated are a periodic potential and a parity-symmetric sextic triple-well potential. Through the quantitative analyses on the non-perturbative contributions to the spectra by the use of the valley method, we show how the characteristic features of N-fold supersymmetry which have been previously reported by the authors can be observed. We also clarify the difference between quasi-exactly solvable and quasi-perturbatively solvable case in view of the dynamical property, that is, dynamical N-fold supersymmetry breaking.Comment: 32 pages, 10 figures, REVTeX

Loop Variables and Gauge Invariant Interactions - I

We describe a method of writing down interacting equations for all the modes of the bosonic open string. It is a generalization of the loop variable approach that was used earlier for the free, and lowest order interacting cases. The generalization involves, as before, the introduction of a parameter to label the different strings involved in an interaction. The interacting string has thus becomes a ``band'' of finite width. The interaction equations expressed in terms of loop variables, has a simple invariance that is exact even off shell. A consistent definition of space-time fields requires the fields to be functions of all the infinite number of gauge coordinates (in addition to space time coordinates). The theory is formulated in one higher dimension, where the modes appear massless. The dimensional reduction that is needed to make contact with string theory (which has been discussed earlier for the free case) is not discussed here.Comment: 40 pages, Latex. Revised version: some typos corrected. Final version to appear in Int. J. of Mod. Phys.

Pairing correlations in nuclei on the neutron-drip line

Paring correlations in weakly bound nuclei on the edge of neutron drip line is studied by using a three-body model. A density-dependent contact interaction is employed to calculate the ground state of halo nuclei $^{6}$He and $^{11}$Li, as well as a skin nucleus $^{24}$O. Dipole excitations in these nuclei are also studied within the same model. We point out that the di-neutron type correlation plays a dominant role in the halo nuclei $^{6}$He and $^{11}$Li having the coupled spin of the two neutrons $S$=0, while the correlation similar to the BCS type is important in $^{24}$O. Contributions of the spin $S$=1 and S=0 configurations are separately discussed in the low energy dipole excitations.Comment: 6 pages, 12 eps figure

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant

This paper presents the complete QED contribution to the electron g-2 up to the tenth order. With the help of the automatic code generator, we have evaluated all 12672 diagrams of the tenth-order diagrams and obtained 9.16 (58)(\alpha/\pi)^5. We have also improved the eighth-order contribution obtaining -1.9097(20)(\alpha/\pi)^4, which includes the mass-dependent contributions. These results lead to a_e(theory)=1 159 652 181.78 (77) \times 10^{-12}. The improved value of the fine-structure constant \alpha^{-1} = 137.035 999 174 (35) [0.25 ppb] is also derived from the theory and measurement of a_e.Comment: 4 pages, 2 figures. Some numbers are slightly change

Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page

Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.Comment: 33 pages, 10 figures; minor corrections, reference added. arXiv admin note: substantial text overlap with arXiv:1007.088

Cluster structure in stable and unstable nuclei

Cluster structure in stable and unstable nuclei has been studied. We report recent developments of theoretical studies on cluster aspect, which is essential for structure study of light unstable nuclei. We discuss negative parity bands in even-even Be and Ne isotopes and show the importance of cluster aspect. Three-body cluster structure and cluster crystallization are also introduced. It was found that the coexistence of cluster and mean-field aspect brings a variety of structures to unstable nuclei.Comment: 6 pages, 3 figures, submitted to Euro. Phys. J.