Mixed basis matrix elements for the subgroup reductions of SO(2,1)

By using the irreducible decomposition on the two-dimensional light cone, the mixed basis matrix elements for the three subgroup reductions of SO(2,1) are calculated. These matrix elements are calculated for the principal series only and can be expressed in terms of well-known special functions. As a consequence of appearing in this context, some new properties of these special functions are given

Unitary Representations of the Homogeneous Lorentz Group in an O(1,1) O(2) Basis and Some Applications to Relativistic Equations

Unitary irreducible representations of the homogeneous Lorentz group O(3, 1) belonging to the principal series are reduced with respect to the subgroup O(1,1) O(2). As an application we determine the mixed basis matrix elements between O(3) and O(1,1) O(2) bases and derive recurrence relations for them. This set of functions is then used to obtain invariant expansions of solutions of the Dirac and Proca free field equations. These expansions are shown to have the correct nonrelativistic limit

Massless BTZ black holes in minisuperspace

We study aspects of the propagation of strings on BTZ black holes. After performing a careful analysis of the global spacetime structure of generic BTZ black holes, and its relation to the geometry of the SL(2,R) group manifold, we focus on the simplest case of the massless BTZ black hole. We study the SL(2,R) Wess-Zumino-Witten model in the worldsheet minisuperspace limit, taking into account special features associated to the Lorentzian signature of spacetime. We analyse the two- and three-point functions in the pointparticle limit. To lay bare the underlying group structure of the correlation functions, we derive new results on Clebsch-Gordan coefficients for SL(2,R) in a parabolic basis. We comment on the application of our results to string theory in singular time-dependent orbifolds, and to a Lorentzian version of the AdS/CFT correspondence.Comment: 28 pages, v2: reference adde

Плотность простатического специфического антигена как прогностический фактор безрецидивной выживаемости у больных локализованным раком предстательной железы, перенесших комбинированное гормонолучевое лечение

Background. Prostate cancer is amongst one of the most prevalent cancers in men worldwide. Combined hormonal-radiation therapy has become a standard of care for localized prostate cancer definitive treatment. As many as 30 % of men are at risk for disease progression within 10 years following radical treatment.Aim. To assess the significance of prostate-specific antigen (PSA) density as a predictor of recurrence-free survival following combined hormonal-radiation therapy in patients with localized prostate cancer.Materials and methods. We conducted a retrospective study of 272 patients with clinically localized prostate cancer treatment results who received combined hormonal-radiation therapy between January 1996 and December 2016.Results. On the basis of our study, we confirmed high prognostic value of PSA density among patients with localized prostate cancer who received combined hormonal-radiation treatment. We utilized ROC-analysis in order to determine the threshold value of the PSA density index – 0.376 ng/ml/cm3, exceeding of which was associated with statistically significant reduction in the recurrence-free survival rate. The area under the curve was 0.711 (95 % confidence interval 0.653–0.764; p <0.0001). The risk of recurrence increased with rising of PSA density.Conclusion. PSA density has proven to be a reliable tool for assessing the risk of prostate cancer recurrence among patients with localized prostate cancer who have undergone combined hormonal-radiation therapy.Введение. Рак предстательной железы является одним из наиболее распространенных онкологических заболеваний. Комбинированная гормонолучевая терапия относится к основным методам радикального лечения рака предстательной железы. У 30 % мужчин возникает прогрессирование заболевания в течение 10 лет после радикального лечения.Цель исследования – определение значимости плотности простатического специфического антигена (ПСА) в качестве предиктора безрецидивной выживаемости после перенесенного комбинированного гормонолучевого лечения у больных локализованным раком предстательной железы.Материалы и методы. В целях оценки клинической и прогностической значимости параметра плотности ПСА проведено ретроспективное исследование результатов лечения 272 пациентов, перенесших комбинированную гормонолучевую терапию в период с января 1996 г. по декабрь 2016 г.Результаты. Установлено прогностическое значение плотности ПСА у больных локализованным раком предстательной железы, получивших комбинированное гормонолучевое лечение. С помощью ROC-анализа определено пороговое значение показателя плотности ПСА – 0,376 нг/мл/см3, превышение которого связано со статистически значимым снижением уровня безрецидивной выживаемости. Площадь под ROC-кривой (AUC) составила 0,711 (95 % доверительный интервал 0,653–0,764; p <0,0001). Риск возникновения рецидива возрастал по мере увеличения показателя плотности ПСА.Заключение. Плотность ПСА, обладая высокими показателями клинической и прогностической значимости, представляет собой надежный инструмент оценки риска возникновения рецидива рака предстательной железы у пациентов, перенесших комбинированное гормонолучевое лечение

Boosting Wigner's nj-symbols

35 pages, many figures. v2: many improvements, in particular clarifications on different options for the phases of the CG coefficientsInternational audienceWe study the SL(2,C) Clebsch-Gordan coefficients appearing in the lorentzian EPRL spin foam amplitudes for loop quantum gravity. We show how the amplitudes decompose into SU(2) nj-symbols at the vertices and integrals over boosts at the edges. The integrals define edge amplitudes that can be evaluated analytically using and adapting results in the literature, leading to a pure state sum model formulation. This procedure introduces virtual representations which, in a manner reminiscent to virtual momenta in Feynman amplitudes, are off-shell of the simplicity constraints present in the theory, but with the integrands that peak at the on-shell values. We point out some properties of the edge amplitudes which are helpful for numerical and analytical evaluations of spin foam amplitudes, and suggest among other things a simpler model useful for calculations of certain lowest order amplitudes. As an application, we estimate the large spin scaling behaviour of the simpler model, on a closed foam with all 4-valent edges and Euler characteristic X, to be N^(X - 5E + V/2). The paper contains a review and an extension of results on SL(2,C) Clebsch-Gordan coefficients among unitary representations of the principal series that can be useful beyond their application to quantum gravity considered here