453 research outputs found

    Holography for the Lorentz Group Racah Coefficients

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    A known realization of the Lorentz group Racah coefficients is given by an integral of a product of 6 ``propagators'' over 4 copies of the hyperbolic space. These are ``bulk-to-bulk'' propagators in that they are functions of two points in the hyperbolic space. It is known that the bulk-to-bulk propagator can be constructed out of two bulk-to-boundary ones. We point out that there is another way to obtain the same object. Namely, one can use two bulk-to-boundary and one boundary-to-boundary propagator. Starting from this construction and carrying out the bulk integrals we obtain a realization of the Racah coefficients that is ``holographic'' in the sense that it only involves boundary objects. This holographic realization admits a geometric interpretation in terms of an ``extended'' tetrahedron.Comment: 12 pages, 2 figures; v2: minor changes; v3: "extended" tetrahedron interpretation adde

    Adapting data collection methods in the Australian life histories and health survey: a retrospective life course study

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    OBJECTIVE Ideally, life course data are collected prospectively through an ongoing longitudinal study. We report adaptive multimethod fieldwork procedures that gathered life history data by mail survey and telephone interview, comparable with the face-to-face methods employed in the English Longitudinal Study on Ageing (ELSA). DESIGN The Australian Life Histories and Health (LHH) Survey was a substudy of the Australian 45 and Up Study, with data collection methods modified from the ELSA Study. A self-complete questionnaire and life history calendar were completed by the participants, followed by a computer-assisted telephone interview recording key life events. RESULTS The LHH survey developed and tested procedures and instruments that gathered rich life history data within an ongoing Australian longitudinal survey on ageing. Data collection proved to be economical. The use of a self-complete questionnaire in conjunction with a life history calendar and coordinated computer-assisted telephone interview was successful in collecting retrospective life course information, in terms of being thorough, practical and efficient. This study has a diverse collection of data covering the life course, starting with early life experiences and continuing with socioeconomic and health exposures and outcomes during adult life. CONCLUSIONS Mail and telephone methodology can accurately and economically add a life history dimension to an ongoing longitudinal survey. The method is particularly valuable for surveying widely dispersed populations. The results will facilitate understanding of the social determinants of health by gathering data on earlier life exposures as well as comparative data across geographical and societal contexts.Supported by an Australian Research Council Grant (DP 1096778, “Socio-economic determinants and health inequalities over the life-course: Australian and English comparisons”) with investigators from the Universities of Sydney, Newcastle and Queensland (Australia) and the University of Manchester (UK)

    Managing plagiarism in programming assignments with blended assessment and randomisation.

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    Plagiarism is a common concern for coursework in many situations, particularly where electronic solutions can be provided e.g. computer programs, and leads to unreliability of assessment. Written exams are often used to try to deal with this, and to increase reliability, but at the expense of validity. One solution, outlined in this paper, is to randomise the work that is set for students so that it is very unlikely that any two students will be working on exactly the same problem set. This also helps to address the issue of students trying to outsource their work by paying external people to complete their assignments for them. We examine the effectiveness of this approach and others (including blended assessment) by analysing the spread of similarity scores across four different introductory programming assignments to find the natural similarity i.e. the level of similarity that could reasonably occur without plagiarism. The results of the study indicate that divergent assessment (having more than one possible solution) as opposed to convergent assessment (only one solution) is the dominant factor in natural similarity. A key area for further work is to apply the analysis to a larger sample of programming assignments to better understand the impact of different features of the assignment design on natural similarity and hence the detection of plagiarism

    New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split

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    I show how there is an ambiguity in how one treats auxiliary variables in gauge theories including general relativity cast as 3 + 1 geometrodynamics. Auxiliary variables may be treated pre-variationally as multiplier coordinates or as the velocities corresponding to cyclic coordinates. The latter treatment works through the physical meaninglessness of auxiliary variables' values applying also to the end points (or end spatial hypersurfaces) of the variation, so that these are free rather than fixed. [This is also known as variation with natural boundary conditions.] Further principles of dynamics workings such as Routhian reduction and the Dirac procedure are shown to have parallel counterparts for this new formalism. One advantage of the new scheme is that the corresponding actions are more manifestly relational. While the electric potential is usually regarded as a multiplier coordinate and Arnowitt, Deser and Misner have regarded the lapse and shift likewise, this paper's scheme considers new {\it flux}, {\it instant} and {\it grid} variables whose corresponding velocities are, respectively, the abovementioned previously used variables. This paper's way of thinking about gauge theory furthermore admits interesting generalizations, which shall be provided in a second paper.Comment: 11 page

    Are Horned Particles the Climax of Hawking Evaporation?

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    We investigate the proposal by Callan, Giddings, Harvey and Strominger (CGHS) that two dimensional quantum fluctuations can eliminate the singularities and horizons formed by matter collapsing on the nonsingular extremal black hole of dilaton gravity. We argue that this scenario could in principle resolve all of the paradoxes connected with Hawking evaporation of black holes. However, we show that the generic solution of the model of CGHS is singular. We propose modifications of their model which may allow the scenario to be realized in a consistent manner.Comment: 26 page

    Triangleland. I. Classical dynamics with exchange of relative angular momentum

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    In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics from relational premises. This is of interest in the absolute versus relative motion debate and also shares a number of features with the geometrodynamical formulation of general relativity, making it suitable for some modelling of the problem of time in quantum gravity. I also study similarity relational particle mechanics (`dynamics of pure shape'), in which only relative times, relative angles and {\sl ratios of} relative separations are meaningful. This I consider firstly as it is simpler, particularly in 1 and 2 d, for which the configuration space geometry turns out to be well-known, e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail. Secondly, the similarity model occurs as a sub-model within the Euclidean model: that admits a shape--scale split. For harmonic oscillator like potentials, similarity triangleland model turns out to have the same mathematics as a family of rigid rotor problems, while the Euclidean case turns out to have parallels with the Kepler--Coulomb problem in spherical and parabolic coordinates. Previous work on relational mechanics covered cases where the constituent subsystems do not exchange relative angular momentum, which is a simplifying (but in some ways undesirable) feature paralleling centrality in ordinary mechanics. In this paper I lift this restriction. In each case I reduce the relational problem to a standard one, thus obtain various exact, asymptotic and numerical solutions, and then recast these into the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure

    Black Hole Remnants and the Information Puzzle

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    Magnetically charged dilatonic black holes have a perturbatively infinite ground state degeneracy associated with an infinite volume throat region of the geometry. A simple argument based on causality is given that these states do not have a description as ordinary massive particles in a low-energy effective field theory. Pair production of magnetic black holes in a weak magnetic field is estimated in a weakly-coupled semiclassical expansion about an instanton and found to be finite, despite the infinite degeneracy of states. This suggests that these states may store the information apparently lost in black hole scattering processes.Comment: 16 pages, revision has 5 figures uuencode
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