Symmetries and Motions in Manifolds

In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the concept of Killing tensors. Via their Poisson brackets these tensors generate an {\em a priori} infinite-dimensional Lie algebra. The nature of such infinite algebras is clarified using the example of flat space-time. Next the formalism is extended to spinning space, which in addition to the standard real co-ordinates is parametrized also by Grassmann-valued vector variables. The equations for extremal trajectories (`geodesics') of these spaces describe the pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve for the motion of a pseudo-classical electron in Schwarzschild space-time.Comment: 19 pages. Lectures at 28th Winter School of Theoretical Physics, Karpacz (Poland, 1992) by J.W. van Holte

Near-source error sensor strategies for active vibration isolation of machines

Due to lightweight construction of vehicles and ships, the reduction of structure borne interior noise problems with passive isolation of engine vibrations might be not sufficient. To improve the isolation, a combination of passive and active isolation techniques can be used (so-called hybrid isolation). This paper focusses on the influence of the sensor positions on the performance of the active isolation. In general two strategies can be distinguished: sensors located in the accommodation with a direct minimization of the sound field and sensors located near the source of vibration. In this paper attention will be paid to an effective weighting of the near-source sensors in such a way that the interior noise in the vehicle is reduced. Also the nearsource strategy of minimization of the injected power is considered. The latter strategy is theoretically very attractive, but is much more difficult to implement in practice. The techniques are explained and compared to each other with the help of numerical models

SUSY in the sky

Spinning particles in curved space-time can have fermionic symmetries generated by the square root of bosonic constants of motion other than the Hamiltonian. We present a general analysis of the conditions under which such new supersymmetries appear, and discuss the Poisson-Dirac algebra of the resulting set of charges, including the conditions of closure of the new algebra. An example of a new non-trivial supersymmetry is found in black-hole solutions of the Kerr-Newman type and corresponds to the Killing-Yano tensor, which plays an important role in solving the Dirac equation in these black-hole metrics.Comment: 28, NIKHEF-H/93-04 and DAMTP R92/4

Supersymmetry and the Geometry of Taub-NUT

The supersymmetric extension of Taub-NUT space admits 4 standard supersymmetries plus several additional non-standard ones. The geometrical origin of these symmetries is traced. The result has applications to fermion modes in gravitational instantons as well as in long-range monopole dynamics.Comment: 9 pages, NIKHEF-H/94-2

The Implementation of Families First in the Netherlands: A One Year Follow-up [IF: 0.725]

Contains fulltext : 63625.pdf (publisher's version ) (Closed access)This study examined whether the American family preservation program Families First was successfully implemented in the Netherlands. Data were collected on 250 children of 177 families who received Families First. At the start of treatment 78% of the children appeared to have serious behavioral problems, 67% of the parents experienced a high level of parental stress, and 63% of the children went through a substantial number of life events during the year preceding the treatment. On average the treatments had the intended duration (about 4 weeks), intensity (about 10 hours a week) and availability (during working hours as well as in evenings and in weekends), and family workers did adhere to important guidelines of treatment delivery. One year after treatment 76% of the children were still living at home. Moreover, children's behavioral problems, parental stress and the number of life events turned out to be significantly decreased. It was concluded that Families First had reached its intended target group, delivered the treatment as intended, and achieved its intended outcomes, suggesting a successful implementation in the Netherlands

Calogero-Vasiliev Oscillator in Dynamically Evolving Curved Spacetime

In a recent work, the consequences of quantizing a real scalar field $\Phi$ according to generalized ``quon'' statistics in a dynamically evolving curved spacetime (~which, prior to some initial time and subsequent to some later time, is flat~) were considered. Here a similar calculation is performed; this time we quantize $\Phi$ via the Calogero-Vasiliev oscillator algebra, described by a real parameter $\nu > -1/2$. It is found that both conservation ( $\nu \rightarrow \nu$ ) and anticonservation ( $\nu \rightarrow - \nu$ ) of statistics is allowed. We find that for mathematical consistency the Bogoliubov coefficients associated with the $i$'th field mode must satisfy $|\alpha_i |^2 - | \beta_i |^2 = 1$ with $| \beta_i |^2$ taking an integer value.Comment: 11 pages ( no figures ), RevTex - To appear in Physics Letters

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(\lambda=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.Comment: 22 pages. 9 figure

Propagators and Path Integrals

Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role of world-line reparametrization invariance of the classical action and the implementation of the corresponding BRST-symmetry in the quantum theory are discussed. The presence of classical world-line supersymmetry is shown to lead to an unwanted doubling of states for massive spin-1/2 particles. The origin of this phenomenon is traced to a `hidden' topological fermionic excitation. A different formulation of the pseudo-classical mechanics using a bosonic representation of \gam_5 is shown to remove these extra states at the expense of losing manifest supersymmetry.Comment: 35 pages, latex, no figures, additional references; to be published in Nucl. Phys.