Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Quantitative spectroscopy of extreme helium stars - Model atmospheres and a non-LTE abundance analysis of BD+10∘^\circ2179?

Extreme helium stars (EHe stars) are hydrogen-deficient supergiants of spectral type A and B. They are believed to result from mergers in double degenerate systems. In this paper we present a detailed quantitative non-LTE spectral analysis for BD+10$^\circ$2179, a prototype of this rare class of stars, using UVES and FEROS spectra covering the range from $\sim$3100 to 10 000 {\AA}. Atmosphere model computations were improved in two ways. First, since the UV metal line blanketing has a strong impact on the temperature-density stratification, we used the Atlas12 code. Additionally, We tested Atlas12 against the benchmark code Sterne3, and found only small differences in the temperature and density stratifications, and good agreement with the spectral energy distributions. Second, 12 chemical species were treated in non-LTE. Pronounced non-LTE effects occur in individual spectral lines but, for the majority, the effects are moderate to small. The spectroscopic parameters give $T_\mathrm{eff}$ = 17 300$\pm$300 K and $\log g$ = 2.80$\pm$0.10, and an evolutionary mass of 0.55$\pm$0.05 $M_\odot$. The star is thus slightly hotter, more compact and less massive than found in previous studies. The kinematic properties imply a thick-disk membership, which is consistent with the metallicity $[$Fe/H$]\approx-1$ and $\alpha$-enhancement. The refined light-element abundances are consistent with the white dwarf merger scenario. We further discuss the observed helium spectrum in an appendix, detecting dipole-allowed transitions from about 150 multiplets plus the most comprehensive set of known/predicted isolated forbidden components to date. Moreover, a so far unreported series of pronounced forbidden He I components is detected in the optical-UV.Comment: Accepted for publication in MNRAS, 26 pages, 19 Figure

Assumptions that imply quantum dynamics is linear

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and states are described by the usual linear structures of quantum mechanics. Beyond that, the proof assumes only that the dynamics does not depend on anything outside the system but must allow the system to be described as part of a larger system. The basic linearity is linked with previously established results to complete a simple derivation of the linear Schrodinger equation. For this it is assumed that density matrices are mapped one-to-one onto density matrices. An alternative is to assume that pure states are mapped one-to-one onto pure states and that entropy does not decrease.Comment: 10 pages. Added references. Improved discussion of equations of motion for mean values. Expanded Introductio

Beyond happiness: Building a science of discrete positive emotions.

While trait positive emotionality and state positive-valence affect have long been the subject of intense study, the importance of differentiating among several "discrete" positive emotions has only recently begun to receive serious attention. In this article, we synthesize existing literature on positive emotion differentiation, proposing that the positive emotions are best described as branches of a "family tree" emerging from a common ancestor mediating adaptive management of fitness-critical resources (e.g., food). Examples are presented of research indicating the importance of differentiating several positive emotion constructs. We then offer a new theoretical framework, built upon a foundation of phylogenetic, neuroscience, and behavioral evidence, that accounts for core features as well as mechanisms for differentiation. We propose several directions for future research suggested by this framework and develop implications for the application of positive emotion research to translational issues in clinical psychology and the science of behavior change. (PsycINFO Database Recor

On the degrees of freedom of the smoothing parameter

The smoothing parameters in a semiparametric model are estimated based on criteria such as generalized cross-validation or restricted maximum likelihood. As these parameters are estimated in a data driven manner they influence the degrees of freedom of a semiparametric model, based on Stein’s lemma. This allows us to associate parts of the degrees of freedom of a semiparametric model to the smoothing parameters. A framework is introduced that enables these degrees of freedom of the smoothing parameters to be derived analytically, based on the implicit function theorem. The degrees of freedom of the smoothing parameters are efficient to compute and have a geometrical interpretation. The practical importance of this finding is highlighted by a simulation study and an application, showing that ignoring the degrees of freedom of the smoothing parameters in AIC based model selection, leads to an increase in the post selection prediction error

Lithostratigraphy, sedimentation and evolution of the Volta Basin in Ghana

We present a revised lithostratigraphy for the Voltaian Supergroup of Ghana, based on a review of existing literature, interpretations of remotely sensed data and reconnaissance field survey of the Volta Basin. These strata thicken eastwards, to a maximum of between 5 and 6 km adjacent to the Pan-African Dahomeyide orogen. They began to accumulate some time after about 1000 Ma, along the margin of an epicontinental sea. Initial sedimentation, comprising the age-equivalent Kwahu and Bombouaka Groups, shows a cyclical mode of deposition controlled by eustatic changes in sea-level that produced a range of nearshore marine, littoral and terrestrial environments. A major erosional interval was followed by deposition of the 3–4 km thick Oti-Pendjari Group. Basal tillites and associated sandy diamictons are correlated with the Marinoan (end-Cryogenian) glaciation, indicating a maximum depositional age of about 635 Ma. The overlying cap carbonates and tuffs were deposited within a shallow epeiric sea bordered by a volcanically active rift system. The main part of the group records the transition from a rifted passive margin to a fully developed foreland basin receiving marine flysch in the form of argillaceous strata interbedded with highly immature wacke-type sandstones and conglomerates. Maximum accommodation space was developed within a foredeep adjacent to the Dahomeyide belt. Towards the end of the orogenic phase, the foredeep succession became partially inverted and then was buried under coarse terrestrial, red-bed molasse of the Obosum Group

Purification of Single-photon Entanglement

Single-photon entanglement is a simple form of entanglement that exists between two spatial modes sharing a single photon. Despite its elementary form, it provides a resource as useful as polarization-entangled photons and it can be used for quantum teleportation and entanglement swapping operations. Here, we report the first experiment where single-photon entanglement is purified with a simple linear-optics based protocol. Besides its conceptual interest, this result might find applications in long distance quantum communication based on quantum repeaters.Comment: Main article: 5 pages, 4 figure