"Root" Action for N=4 Supersymmetric Mechanics Theories

We propose to consider the N=4,d=1 supermultiplet with $% (4,4,0) component content as a ``root'' one. We elaborate a new reduction scheme from the ``root'' multiplet to supermultiplets with a smaller number of physical bosons. Starting from the most general sigma-model type action for the ``root'' multiplet, we explicitly demonstrate that the actions for the rest of linear and nonlinear N=4 supermultiplets can be easily obtained by reduction. Within the proposed reduction scheme there is a natural possibility to introduce Fayet-Iliopoulos terms. In the reduced systems, such terms give rise to potential terms, and in some cases also to terms describing the interaction with a magnetic field. We demonstrate that known N=4 superconformal actions, together with their possible interactions, appear as results of the reduction from a free action for the ``root'' supermultiplet. As a byproduct, we also construct an N=4 supersymmetric action for the linear (3,4,1) supermultiplet, containing both an interaction with a Dirac monopole and a harmonic oscillator-type potential, generalized for arbitrary conformally flat metrics.Comment: 12 page

Motion of a spin 1/2 particle in shape invariant scalar and magnetic fields

We study the motion of a spin 1/2 particle in a scalar as well as a magnetic field within the framework of supersymmetric quantum mechanics(SUSYQM). We also introduce the concept of shape invariant scalar and magnetic fields and it is shown that the problem admits exact analytical solutions when such fields are considered.Comment: 14 page

Pauli equation and the method of supersymmetric factorization

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary 2-dimensional SUSY QM quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given.Comment: 18 pages, Late

A Generalization of the Bargmann-Fock Representation to Supersymmetry by Holomorphic Differential Geometry

In the Bargmann-Fock representation the coordinates $z^i$ act as bosonic creation operators while the partial derivatives $\partial_{z^j}$ act as annihilation operators on holomorphic $0$-forms as states of a $D$-dimensional bosonic oscillator. Considering also $p$-forms and further geometrical objects as the exterior derivative and Lie derivatives on a holomorphic ${\bf C}^D$, we end up with an analogous representation for the $D$-dimensional supersymmetric oscillator. In particular, the supersymmetry multiplet structure of the Hilbert space corresponds to the cohomology of the exterior derivative. In addition, a 1-complex parameter group emerges naturally and contains both time evolution and a homotopy related to cohomology. Emphasis is on calculus.Comment: 11 pages, LaTe

A nuclear factor 1 binding site mediates the transcriptional activation of a type I collagen promoter by transforming growth factor-beta

Transforming growth factor-beta (TGF-beta) increases the steady-state RNA levels of several fibroblast extracellular matrix proteins. Using DNA transfection, we show that TGF-beta stimulates the activity of the mouse alpha 2(l) collagen promoter 5- to 10-fold in mouse NIH 3T3 and rat osteosarcoma cells. Deletion analysis indicates that a segment of this promoter between -350 and -300, overlapping a nuclear factor 1 (NF1) binding site, is needed for TGF-beta stimulation. A 3 bp substitution mutation abolishing NF1 binding to this site inhibits TGF-beta activation. Insertion of this NF1 binding site 5' to the SV40 early promoter makes the promoter TGF-beta inducible, but the 3 bp substitution does not. Similarly, when the NF1 binding site at the replication origin of adenovirus 2 and 5 is inserted 5' to the SV40 promoter, the promoter responds to TGF-beta. Therefore an NF1 binding site mediates the transcriptional activation of the mouse alpha 2(l) collagen promoter by TGF-beta

Photoproduction evidence for and against hidden-strangeness states near 2 GeV

Experimental evidence from coherent diffractive proton scattering has been reported for two narrow baryonic resonances which decay predominantly to strange particles. These states, with masses close to 2.0 GeV would, if confirmed, be candidates for hidden strangeness states with unusual internal structure. In this paper we examine the literature on strangeness photoproduction, to seek additional evidence for or against these states. We find that one state is not confirmed, while for the other state there is some mild supporting evidence favoring its existence. New experiments are called for, and the expected photoproduction lineshapes are calculated.Comment: 9 pages, RevTex, five postscript figures, submitted to PR

Do weak institutions prolong crises? : On the identification, characteristics, and duration of declines during economic slumps

This working paper is part of the research programme on ‘Institutions, Governance and Long‐term Economic Growth’, a partnership between the French Development Agency (AFD) and the Maastricht Graduate School of Governance (Maastricht University - UNU-Merit). The research builds on the Institutional Profiles Database IPD, jointly developed by AFD and the French Ministry of the Economy since 2001

Extended Supersymmetries and the Dirac Operator

We consider supersymmetric quantum mechanical systems in arbitrary dimensions on curved spaces with nontrivial gauge fields. The square of the Dirac operator serves as Hamiltonian. We derive a relation between the number of supercharges that exist and restrictions on the geometry of the underlying spaces as well as the admissible gauge field configurations. From the superalgebra with two or more real supercharges we infer the existence of integrability conditions and obtain a corresponding superpotential. This potential can be used to deform the supercharges and to determine zero modes of the Dirac operator. The general results are applied to the Kahler spaces CP^n.Comment: 22 pages, no figure

The XX--model with boundaries. Part I: Diagonalization of the finite chain

This is the first of three papers dealing with the XX finite quantum chain with arbitrary, not necessarily hermitian, boundary terms. This extends previous work where the periodic or diagonal boundary terms were considered. In order to find the spectrum and wave-functions an auxiliary quantum chain is examined which is quadratic in fermionic creation and annihilation operators and hence diagonalizable. The secular equation is in general complicated but several cases were found when it can be solved analytically. For these cases the ground-state energies are given. The appearance of boundary states is also discussed and in view to the applications considered in the next papers, the one and two-point functions are expressed in terms of Pfaffians.Comment: 56 pages, LaTeX, some minor correction