Austrian Academy of Sciences

Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften
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    Connecting in the Dirac Equation the Clifford Algebra of Lorentz Invariance with the Lie Algebra of SU(N) Gauge Symmetry

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    In this paper, we study possible mathematical connections of the Clifford algebra with the su(N)-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal SU(N) gauge-symmetry for a massive spin one-half fermion described by the Dirac equation. The related matrix algebra is worked out in particular for the SU(2) symmetry and outlined as well for the color gauge group SU(3). Possible perspectives of this approach to unification of symmetries are briefly discussed. The calculations make extensive use of tensor multiplication of the matrices involved, whereby our focus is on revisiting the Coleman–Mandula theorem. This permits us to construct unified symmetries between Lorentz invariance and gauge symmetry in a direct product sense

    IV Good-Practice-Empfehlungen

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    Loh, Anton

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    * 1.10.1845 Udritsch/Böhmen (Údrč/CZ), † 24.7.1890 Gmunden/OÖ Geiger und Bratschist

    Friedl, Familie

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    Hans (Johann): * 23.8.1874 Oberkappel/OÖ, † 18.11.1943 Putzleinsdorf/OÖ. Pädagoge, Chorleiter, Kapellmeister

    Estimating Population Counts with Capture-Recapture Models in the Context of Erroneous Records in Linked Administrative Data

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    In the absence of a traditional census and a comprehensive population register (as it is thecase in the UK), administrative data sources, i.e. health, school or tax records, can offer analternative to estimate the size of residence population. However, such data sources are designedto capture information only from specific populations which imposes a challenge to theestimation. A suitable method to overcome the challenge is to link administrative data sourcesthat collect information from different but overlapping populations and use capture-recapturemodels to estimate the population counts. There are various assumptions required to obtainunbiased estimates by using capture-recapture models. In practice, especially the assumptionson ‘homogeneous inclusion probabilities’ and ‘no over coverage’ are often not met. This paperproposes a two-step procedure for estimating population counts with capture-recapture modelsthat account for heterogeneity of inclusion probabilities and the over coverage in the datasources. We apply our methodology to the linked Patient Register and Customer InformationSystem dataset which violates both of the aforementioned assumptions. The Patient Registerincludes people who are registered with a National Health Service General Practitioner doctor.In 2011, the Patient Register overestimated the size of England and Wales populationby 4.3% (over coverage) and its sex ratio was different than the 2011 Census estimates (heterogeneousof inclusion probabilities). The Customer Information System dataset providesinformation on all individuals who have ever had a national insurance number and childrenwhose parents have made a child benefit claim relating to them. In 2011, it over estimatedthe size of England and Wales population by 9.5% and its age and sex structure was differentthan the 2011 Census estimates. Applying our approach, we estimate population counts ofthe South East region of England by age, sex and local authority, and compare them withcensus estimates using percentage difference maps

    Der Kaiser mit der Tiara. Spiegelungen und Wandlungen des ersten Romzuges Friedrichs III. in der italienischen Kunst. Römische Historische Mitteilungen|Römische Historische Mitteilungen 63|

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    The journey to Rome which Frederick III undertook for his coronation as emperor was portrayed in a number of works of art, which were conceived along the route through Italy. However, these works of art were meant to serve as propaganda for the emperor only indirectly. As a matter of fact, those commissioning the works considered the symbolic power of the events and the authority of the Imperator Romanorum far more important in terms of ‘self-portrayal’. These works of art were indeed commissioned to celebrate the numerous promotions to the aristocracy or to a higher position within the aristocracy that Frederick III performed during his journey. Through the images depicted on medals and on illuminated manuscripts, the ennobled ones, who commissioned these works, aimed at associating their personal image and their memoria with the emperor. Particularly noteworthy are the panels of two cassoni, where Frederick’s two-day journey, his stay in Florence and the crowning ceremonies in Rome are depicted in multiple scenes. The cassoni were commissioned by the Medici family for Orlando de Medici, upon whom a knighthood was conferred by the emperor and who most likely participated in the crowning ceremony in Rome. However, a differentiated approach must be adopted in order to analyse the realistic representation of the pictures: on the one hand, these pictures have an important documentary value, whereby the topographical factors are also taken into account. On the other hand, they deviate significantly from the historical facts. One of the most striking differences lies in the central motif of the crown used by the pope during the ceremony, which does not reflect the standard type of the emperor’s crown but is portrayed as a variation of the papal tiara. The real intention behind this kind of choice remains unknown, but it does illustrate the cultural clashes related to the public’s perception of this ceremony which was to be the last coronation of an emperor performed in Rome by a pope

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    Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschaften is based in Austria
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