Refining the classification of the irreps of the 1D N-Extended Supersymmetry

The linear finite irreducible representations of the algebra of the 1D $N$-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The classification of the irreducible representations with the same fields content and different connectivity is presented up to $N\leq 8$.Comment: Two extra cases added. Reply to hep-th/0611060v2 comments adde

Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets

We furnish an algebraic understanding of the inequivalent connectivities (computed up to $N\leq 10$) of the graphs associated to the irreducible supermultiplets of the N-extended Supersymmetric Quantum Mechanics. We prove that the inequivalent connectivities of the N=5 and N=9 irreducible supermultiplets are due to inequivalent decompositions into two sets of N=4 (respectively, N=8) supermultiplets. "Oxido-reduction" diagrams linking the irreducible supermultiplets of the N=5,6,7,8 supersymmetries are presented. We briefly discuss these results and their possible applications.Comment: 15 pages, 5 figure

On the spectrum-generating superalgebras of the deformed one-dimensional quantum oscillators

We investigate the dynamical symmetry superalgebras of the one-dimensional Matrix Superconformal Quantum Mechanics with inverse-square potential. They act as spectrum-generating superalgebras for the systems with the addition of the de Alfaro-Fubini-Furlan oscillator term. The undeformed quantum oscillators are expressed by $2^n\times 2^n$ supermatrices; their corresponding spectrum-generating superalgebras are given by the $osp(2n|2)$ series. For $n=1$ the addition of a inverse-square potential does not break the $osp(2|2)$ spectrum-generating superalgebra. For $n=2$ two cases of inverse-square potential deformations arise. The first one produces Klein deformed quantum oscillators; the corresponding spectrum-generating superalgebras are given by the $D(2,1;\alpha)$ class, with $\alpha$ determining the inverse-square potential coupling constants. The second $n=2$ case corresponds to deformed quantum oscillators of non-Klein type. In this case the $osp(4|2)$ spectrum-generating superalgebra of the undeformed theory is broken to $osp(2|2)$. The choice of the Hilbert spaces corresponding to the admissible range of the inverse-square potential coupling constants and the possible direct sum of lowest weight representations of the spectrum-generating superalgebras is presented.Comment: Final version to appear in J. Math. Phys.; three references adde

One-dimensional structures behind twisted and untwisted superYang-Mills theory

We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N=1 superYang-Mills theory.Comment: 12 pages. Final version to appear in Lett. Math. Phys. with improved notation and misprints correcte

Determinant Line Bundles and Topological Invariants of Hyperbolic Geometry - Expository Remarks

We give some remarks on twisted determinant line bundles and Chern-Simons topological invariants associated with real hyperbolic manifolds. Index of a twisted Dirac operator is derived. We discuss briefly application of obtained results in topological quantum field theory.Comment: 10 pages. To appear in G@C, special issue devoted to QG, Unified Models and Strings, to mark 100th Anniversary of Tomsk State Pedagogical University. Editor - S.D. Odintso

Supersymmetric Extension of Hopf Maps: N=4 sigma-models and the S^3 -> S^2 Fibration

We discuss four off-shell N=4 D=1 supersymmetry transformations, their associated one-dimensional sigma-models and their mutual relations. They are given by I) the (4,4)_{lin} linear supermultiplet (supersymmetric extension of R^4), II) the (3,4,1)_{lin} linear supermultiplet (supersymmetric extension of R^3), III) the (3,4,1)_{nl} non-linear supermultiplet living on S^3 and IV) the (2,4,2)_{nl} non-linear supermultiplet living on S^2. The I -> II map is the supersymmetric extension of the R^4 -> R^3 bilinear map, while the II -> IV map is the supersymmetric extension of the S^3 -> S^2 first Hopf fibration. The restrictions on the S^3, S^2 spheres are expressed in terms of the stereographic projections. The non-linear supermultiplets, whose supertransformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The sigma-models are determined in terms of an unconstrained prepotential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the prepotential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N<=8.Comment: 24 page

Conditioned reflex activity of rats at later periods after the end of flight aboard the Kosmos-605 biosatellite

The aftereffects of spaceflight on the higher nervous activity of rats were studied. A five lane maze with a feeding terminal was used to check such factors as transfer of experience, the habit and speed of reaching the goal in the maze, long term memory, and the dynamics of errors. During the 3rd-7th postflight week, functional disturbances in the rat HNA were manifested in the deterioration of the capacity for the transfer of experience and for locating the feeding compartment in the maze, thus indicating a general decrease of work capacity. The increased number of errors and failures pointed to exhaustion of higher nervous processes and to the weakened functional activity of the brain