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

Killing tensors and a new geometric duality

We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor. The relation can be generalized to spinning spaces, but only at the expense of introducing torsion. This introduces new supersymmetries in their geometry. Interesting examples in four dimensions include the Kerr-Newman metric of spinning black-holes and self-dual Taub-NUT.Comment: 20 pages (a4), standard LaTeX, no figure

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

Background field boundary conditions for affine Toda field theories

Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities for integrable boundary conditions depending upon the time-derivative of the fields at the boundary but containing no free parameters other than the bulk coupling constant.Comment: 21 pages, harvma

Affine Toda field theory on a half line

The question of the integrability of real-coupling affine toda field theory on a half-line is addressed. It is found, by examining low-spin conserved charges, that the boundary conditions preserving integrability are strongly constrained. In particular, for the $a_n\ (n>1)$ series of models there can be no free parameters introduced by the boundary condition; indeed the only remaining freedom (apart from choosing the simple condition $\partial_1\phi =0$), resides in a choice of signs. For a special case of the boundary condition, it is argued that the classical boundary bound state spectrum is closely related to a consistent set of reflection factors in the quantum field theory.Comment: 16 pages, TEX (harvmac), DTP-94/7, YITP/U-94-1

Pursuing the Real Vancomycin Clearance during Continuous Renal Replacement Therapy in Intensive Care Unit Patients:Is There Adequate Target Attainment?

Introduction: Vancomycin is used in intensive care unit (ICU) patients for the treatment of infections caused by gram-positive bacteria. The vancomycin pharmacokinetic/pharmacodynamic index is a ratio of the area under the concentration to the minimum inhibitory concentration ≥400-600 h∗mg/L. This target can generally be achieved by a plasma concentration of 20-25 mg/L. Together with the pathophysiological alterations and pharmacokinetic variability associated with critical illness, the use of continuous renal replacement therapy (CRRT) may complicate the attainment of adequate vancomycin concentrations. The primary objective was the prevalence of attainment of vancomycin concentrations 20-25 mg/L after 24 h in adult ICU patients receiving CRRT. Secondary outcomes were to evaluate target attainment at days 2 and 3 and to calculate vancomycin clearance (CL) by CRRT and residual diuresis. Methods: We performed a prospective observational study in adult ICU patients on CRRT, which received at least 24 h continuous infusion of vancomycin. Between May 2020 and February 2021, daily vancomycin residual blood gas and dialysate samples were collected from 20 patients, every 6 h and if possible vancomycin urine samples. Vancomycin was analysed with an immunoassay method. The CL by CRRT was calculated by a different approach correcting for the downtime and providing insight into the degree of filter patency. Results: The proportion of patients with vancomycin concentrations &lt;20 mg/L was 50% 24 h after starting vancomycin (n = 10). No differences were observed in patient characteristics. The target vancomycin concentration 20-25 mg/L was only achieved in 30% of the patients. On days 2 and 3, despite the use of TDM and albeit in lower percentages, sub- and supratherapeutic levels were still observed. Taking downtime and filter patency into account resulted in lower vancomycin CL. Conclusions: 50% of the studied ICU patients on CRRT showed subtherapeutic vancomycin concentrations 24 h after starting therapy. The results reveal that optimization of vancomycin dosage during CRRT therapy is needed.</p

De Sitter Cosmic Strings and Supersymmetry

We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.Comment: Version similar to the one accepted by General Relativity and Gravitatio

Stability of circular orbits of spinning particles in Schwarzschild-like space-times

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.Comment: eps figures, submitted to General Relativity and Gravitatio

Background field boundary conditions for affine Toda field theories

Classical integrability is investigated for affine Toda field theories in the presence of a constant background tensor field. This leads to a further set of discrete possibilities containing no free parameters other than the bulk coupling constant