On the Geometry of Supersymmetric Quantum Mechanical Systems

We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.Comment: 18 page

The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

Heat kernel coefficients for chiral bag boundary conditions

We study the asymptotic expansion of the smeared L2-trace of fexp(-tP^2) where P is an operator of Dirac type, f is an auxiliary smooth smearing function which is used to localize the problem, and chiral bag boundary conditions are imposed. Special case calculations, functorial methods and the theory of zeta and eta invariants are used to obtain the boundary part of the heat-kernel coefficients a1 and a2.Comment: Published in J. Phys. A38, 2259-2276 (2005). Record without file already exists on the SLAC recor

Killing spinors in supergravity with 4-fluxes

We study the spinorial Killing equation of supergravity involving a torsion 3-form \T as well as a flux 4-form \F. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We investigate the constraint \T \cdot \Psi = 0, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically

Effective Wess-Zumino-Witten Action for Edge States of Quantum Hall Systems on Bergman Ball

Using a group theory approach, we investigate the basic features of the Landau problem on the Bergman ball {\bf B}^k. This can be done by considering a system of particles living on {\bf B}^k in the presence of an uniform magnetic field B and realizing the ball as the coset space SU(k,1)/U(k). In quantizing the theory on {\bf{B}}^k, we define the wavefunctions as the Wigner \cal{D}-functions satisfying a set of suitable constraints. The corresponding Hamiltonian is mapped in terms of the right translation generators. In the lowest Landau level, we obtain the wavefunctions as the SU(k,1) coherent states. This are used to define the star product, density matrix and excitation potential in higher dimensions. With these ingredients, we construct a generalized effective Wess-Zumino-Witten action for the edge states and discuss their nature.Comment: 19 pages, clarifications and some equations removed, version published in NP

Twisted k-graph algebras associated to Bratteli diagrams

Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are matrix algebras over noncommutative tori. For such systems we calculate the ordered K-theory and the gauge-invariant semifinite traces of the resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the sense of Pask-Raeburn-R{\o}rdam-Sims.Comment: 28 pages, pictures prepared using tik

Supersymmetric Nonlinear O(3) Sigma Model on the Lattice

A supersymmetric extension of the nonlinear O(3) sigma model in two spacetime dimensions is investigated by means of Monte Carlo simulations. We argue that it is impossible to construct a lattice action that implements both the O(3) symmetry as well as at least one supersymmetry exactly at finite lattice spacing. It is shown by explicit calculations that previously proposed discretizations fail to reproduce the exact symmetries of the target manifold in the continuum limit. We provide an alternative lattice action with exact O(3) symmetry and compare two approaches based on different derivative operators. Using the nonlocal SLAC derivative for the quenched model on moderately sized lattices we extract the value {\sigma}(2, u_0) = 1.2604(13) for the step scaling function at u_0 = 1.0595, to be compared with the exact value 1.261210. For the supersymmetric model with SLAC derivative the discrete chiral symmetry is maintained but we encounter strong sign fluctuations, rendering large lattice simulations ineffective. By applying the Wilson prescription, supersymmetry and chiral symmetry are broken explicitly at finite lattice spacing, though there is clear evidence that both are restored in the continuum limit by fine tuning of a single mass parameter.Comment: 35 pages, 36 figures, 2 tables; updated version as accepted by JHE

Providing Alternative Declarative Descriptions for Entity Sets Using Parallel Concept Lattices

We propose an approach for modifying a declarative description of a set of entities (e.g., a SPARQL query) for the purpose of finding alternative declarative descriptions for the entities. Such a shift in representation can help to get new insights into the data, to discover related attributes, or to find a more concise description of the entities of interest. Allowing the alternative descriptions furthermore to be close approximations of the original entity set leads to more flexibility in finding such insights. Our approach is based on the construction of parallel formal concept lattices over different sets of attributes for the same entities. Between the formal concepts in the parallel lattices, we define mappings which constitute approximations of the extent of the concepts. In this paper, we formalise the idea of two types of mappings between parallel concept lattices, provide an implementation of these mappings and evaluate their ability to find alternative descriptions in a scenario of several real-world RDF data sets. In this scenario we use descriptions for entities based on RDF classes and seek for alternative representations based on properties associated with the entities

A Dual Fluorescence–Spin Label Probe for Visualization and Quantification of Target Molecules in Tissue by Multiplexed FLIM–EPR Spectroscopy

Simultaneous visualization and concentration quantification of molecules in biological tissue is an important though challenging goal. The advantages of fluorescence lifetime imaging microscopy (FLIM) for visualization, and electron paramagnetic resonance (EPR) spectroscopy for quantification are complementary. Their combination in a multiplexed approach promises a successful but ambitious strategy because of spin label-mediated fluorescence quenching. Here, we solved this problem and present the molecular design of a dual label (DL) compound comprising a highly fluorescent dye together with an EPR spin probe, which also renders the fluorescence lifetime to be concentration sensitive. The DL can easily be coupled to the biomolecule of choice, enabling in vivo and in vitro applications. This novel approach paves the way for elegant studies ranging from fundamental biological investigations to preclinical drug research, as shown in proof-of-principle penetration experiments in human skin ex vivo