One-Nucleon Effective Generators of the Poincare Group derived from a Field Theory: Mass Renormalization

We start from a Lagrangian describing scalar "nucleons" and mesons which interact through a simple vertex. Okubo's method of unitary transformation is used to describe a single nucleon dressed by its meson cloud. We find an expression for the physical mass of the nucleon being correct up to second order in the coupling constant. It is then verified that this result is the same as the corresponding expression found by Feynman techniques. Finally we also express the three boost operators in terms of the physical nucleon mass. Doing so we find expressions for all the ten generators of Poincar\'e transformations for the system of one single dressed nucleon.Comment: 19 pages, no figure

The structural distortion in antiferromagnetic LaFeAsO investigated by a group-theoretical approach

As experimentally well established, undoped LaFeAsO is antiferromagnetic below 137K with the magnetic moments lying on the Fe sites. We determine the orthorhombic body-centered group Imma (74) as the space group of the experimentally observed magnetic structure in the undistorted lattice, i.e., in a lattice possessing no structural distortions in addition to the magnetostriction. We show that LaFeAsO possesses a partly filled "magnetic band" with Bloch functions that can be unitarily transformed into optimally localized Wannier functions adapted to the space group Imma. This finding is interpreted in the framework of a nonadiabatic extension of the Heisenberg model of magnetism, the nonadiabatic Heisenberg model. Within this model, however, the magnetic structure with the space group Imma is not stable but can be stabilized by a (slight) distortion of the crystal turning the space group Imma into the space group Pnn2 (34). This group-theoretical result is in accordance with the experimentally observed displacements of the Fe and O atoms in LaFeAsO as reported by Clarina de la Cruz et al. [nature 453, 899 (2008)]

Seismology of adolescent neutron stars: Accounting for thermal effects and crust elasticity

We study the oscillations of relativistic stars, incorporating key physics associated with internal composition, thermal gradients and crust elasticity. Our aim is to develop a formalism which is able to account for the state-of-the-art understanding of the complex physics associated with these systems. As a first step, we build models using a modern equation of state including composition gradients and density discontinuities associated with internal phase-transitions (like the crust-core transition and the point where muons first appear in the core). In order to understand the nature of the oscillation spectrum, we carry out cooling simulations to provide realistic snapshots of the temperature distribution in the interior as the star evolves through adolescence. The associated thermal pressure is incorporated in the perturbation analysis, and we discuss the presence of $g$-modes arising as a result of thermal effects. We also consider interface modes due to phase-transitions and the gradual formation of the star's crust and the emergence of a set of shear modes.Comment: 27 pages, 14 figure

Die Bedeutung des Films für die Erforschung des Fortbewegungsvorganges bei den Tieren

The following article by Professor Krüger is a very instructive example of what we otherwhere called "horizontal comparison". Encyclopedic films treating the same topic, but concerning different animals have been used for extensive comparative studies. We think that this example can encourage us to go on with our undertaking and we hope that it will give impulses for further work of similar kind.Der folgende Aufsatz von Herrn Prof. Krüger ist ein sehr aufschlußreiches Beispiel für das, was wir an anderer Stelle einmal als horizontalen Vergleich bezeichnet haben. Filme über das gleiche Thema (die Lokomotion) bei einer großen Anzahl verschiedener Tierarten sind hier zu einer umfassenden vergleichenden Studie zusammengefaßt worden. Wir glauben, daß dieses sehr eindrucksvolle Beispiel uns zum Weiterschreiten auf dem begonnenen Wege ermutigen sollte und hoffen, daß es zu ähnlichen Arbeiten Anregung geben möge.L'article suivant par le Prof. Krüger est un exemple très instructif de ce que nous avons nommé autrefois la comparaison horizontale. On a employé des films encyclopédiques traitant le même thème (la locomotion), mais chez un grand nombre d'animaux différents, pour faire des études comparatives étendues. Nous croyons que cet exemple saisissant doit nous encourager à progresser dans la voie choisie et nous espérons qu'il serve de stimulant pour des travaux analogues

Professor A. J. H. van der Walt- 'n Waardering

My kennismaking met prof. Andries van der Walt dateer vanaf Februarie1925, nou een-en-dertig jaar gelede

Ons erfenis van driehonderd jaar

Waar ons tans die stigting van die blanke volksplanting aan die Kaap driehonderd jaar gelede herdenk, gaan dit nie om bloot in die herinnering terug te roep ’n eenmalige gebeurtenis van April 1652 nie, maar veel meer die uitwerking en gevolge daarvan, soos sigbaar in die Unie van Suid-Afrika vandag

From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces

This paper supplements and partly extends an earlier publication, Phys. Rev. Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the infinite volume ground state configurations (GSCs) of pair interactions \vfi and \vfi+\psi, where \vfi is the inverse Fourier transform of a nonnegative function vanishing outside the sphere of radius $K_0$, and $\psi$ is any nonnegative finite-range interaction of range $r_0\leq\gamma_d/K_0$, where $\gamma_3=\sqrt{6}\pi$. In three dimensions the decay of \vfi can be as slow as $\sim r^{-2}$, and an interaction of asymptotic form $\sim\cos(K_0r+\pi/2)/r^3$ is among the examples. At a dimension-dependent density $\rho_d$ the ground state of \vfi is a unique Bravais lattice, and for higher densities it is continuously degenerate: any union of Bravais lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC. Adding $\psi$ decreases the ground state degeneracy which, nonetheless, remains continuous in the open interval $(\rho_d,\rho_d')$, where $\rho_d'$ is the close-packing density of hard balls of diameter $r_0$. The ground state is unique at both ends of the interval. In three dimensions this unique GSC is the bcc lattice at $\rho_3$ and the fcc lattice at $\rho_3'=\sqrt{2}/r_0^3$.Comment: Published versio