Nilpotent Marsh and SUSY QM

We consider the nilpotent additions to classical trajectories in supersymmetric and nonsupersymmetric theories. The condition of anilpotence of action on some generalized solutions leads to the Witten supersymmetric Lagrangian. The condition of anilpotence of topological charge is the same as one of superpotential with spontaneous broken supersymmetry. We should vanish half of Grassmann constants of integration, because in this case only we obtain the same number of normalized bosonic and fermionic zero modes.Comment: 8 pages, Latex 2.09. Talk given at the conference in memory of V.I. Ogievetski, Dubna, July, 1997. To be published in the Proceeding

Potentials in N=4 superconformal mechanics

Proceeding from nonlinear realizations of (super)conformal symmetries, we explicitly demonstrate that adding the harmonic oscillator potential to the action of conformal mechanics does not break these symmetries but modifies the transformation properties of the (super)fields. We also analyze the possibility to introduce potentials in N=4 supersymmetric mechanics by coupling it with auxiliary fermionic superfields. The new coupling we considered does not introduce new fermionic degrees of freedom - all our additional fermions are purely auxiliary ones. The new bosonic components have a first order kinetic term and therefore they serve as spin degrees of freedom. The resulting system contains, besides the potential term in the bosonic sector, a non-trivial spin-like interaction in the fermionic sector. The superconformal mechanics we constructed in this paper is invariant under the full $D(2,1;\alpha)$ superconformal group. This invariance is not evident and is achieved within modified (super)conformal transformations of the superfields.Comment: 12 pages, PACS number: 12.60.J

Dynamics of (SUSY) AdS Space Isometry Breaking

Actions governing the dynamics of the Nambu-Goldstone modes resulting from the spontaneous breaking of the SO(4,2) and $SU(2,2|1)$ isometries of five dimensional anti-de Sitter space ($AdS_{5}$) and SUSY $AdS_{5}\times S_1$ spaces respectively due to a restriction of the motion to embedded four dimensional $AdS_{4}$ space and four dimensional Minkowski space ($M_4$) probe branes are presented. The dilatonic Nambu-Goldstone mode governing the motion of the $M_4$ space probe brane into the covolume of the SUSY $AdS_5\times S_1$ space is found to be unstable. No such instablility appears in the other cases. Gauging these symmetries leads to an Einstein-Hilbert action containing, in addition to the gravitational vierbein, a massive Abelian vector field coupled to gravity.Comment: 6 pages, 0 figures, to appear in Proceedings of IRGAC 2006: 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelon

Diffeomorphism, kappa transformations and the theory of non-linear realisations

We will show how the theory of non-linear realisations can be used to naturally incorporate world line diffeomorphisms and kappa transformations for the point particle and superpoint particle respectively. Similar results also hold for a general p-brane and super p-brane, however, we must in these cases include an additional Lorentz transformation.Comment: 19pages, no figure. References are added and typos are correcte

Deformed Oscillator Algebras and Higher-Spin Gauge Interactions of Matter Fields in 2+1 Dimensions

We formulate a non-linear system of equations which describe higher-spin gauge interactions of massive matter fields in 2+1 dimensional space-time and explain some properties of the deformed oscillator algebra which underlies this formulation. In particular we show that the parameter of mass $M$ of matter fields is related to the deformation parameter in this algebra.Comment: LaTex, 12 pages, no figures; Invited talk at the International Seminar Supersymmetry and Quantum Field Theory dedicated to the memory of Dmitrij V. Volkov; Kharkov, January 1997; to appear in the proceeding

The Spinning Particles as a Nonlinear Realizations of the Superworldline Reparametrization Invariance

The superdiffeomorphisms invariant description of $N$ - extended spinning particle is constructed in the framework of nonlinear realizations approach. The action is universal for all values of $N$ and describes the time evolution of $D+2$ different group elements of the superdiffeomorphisms group of the $(1,N)$ superspace. The form of this action coincides with the one-dimensional version of the gravity action, analogous to Trautman's one.Comment: 4 pages, RevTe

Water Resources Management In Support Of Raw Region Based On Decoupling Effect

It determines the presence of the decoupling effect in the Russians raw regions materials by using water. Developed models that explain the relationship between the gross regional product and water intake. It proved no effect on the growth of water consumption in most regions of the reference commodity. Recommendations for the decoupling effect development in support of Russians raw regions

Reconstruction of unbroken vasculature of mouse by varying the slope of the scan plane in MRI

Reconstruction of vascular net of small laboratory animals from MRI data is associated with some problems. This paper proposes a method of MRI data processing which allows to eliminate the fragmentation of reconstructed vascular net. Problem of vessels fragmentation occurs in the case when vessels are parallel to the scanning plane. Our approach is based on multiple scanning, object under consideration is probed by several sets of parallel planes. The algorithm is applied to real MRI data of small laboratory animals and shows good results

Nonlinear supersymmetry: from classical to quantum mechanics

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum level. With an example of the system realizing the nonlinear superconformal symmetry, we discuss the nature of such corrections and speculate on their possible general origin.Comment: 11 page

AdS_2/CFT_1, Canonical Transformations and Superconformal Mechanics

We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS_2\times S^2 horizon of an extreme Reissner-Nordstr\"om black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N=4 superparticle on AdS_2\times S^2 background.Comment: 10 pages, LaTe