Superfield formulation of the Lagrangian BRST quantization method

Lagragian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the $S$-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.Comment: 9 pages, Latex, no figure

On the total mean curvature of non-rigid surfaces

Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean curvature of a closed smooth surface in the Euclidean 3-space is stationary under an infinitesimal flex.Comment: 4 page

РЕФЛЕКТОМЕТРИЧЕСКОЕ И ВИЗУАЛЬНО-ТЕСТОВОЕ ОПРЕДЕЛЕНИЕ PD(II) В ОБЪЕКТАХ СЛОЖНОГО СОСТАВА С ИСПОЛЬЗОВАНИЕМ ИНДИКАТОРНОЙ БУМАГИ

RIP-Pd-Test reagent indicator paper based on 1-phenyl-5-(3,4-dihydro-6-methyl-4-oxo-3H-pyrimidin-2-yl)-formazan-6-cellulose has been proposed for determining the palladium content using the sorption-reflectometry and visual-test methods in objects of complex composition. The RIP synthesis technique was described. The estimated composition of the metal complex formed as a result of the heterogeneous indicator reaction at pH 1.5–2.5 was indicated, and the forced coordination of palladium : reagent = 1:1 was ensured. When the RIP interacted with palladium (II) ions, the yellow indicator strip became green with different intensities. Under the selected conditions, the high selectivity for the detection and determination of Pd(II) was shown. With the help of the «Ecotest-2040» portable reflectometer, the reflectometry measurements were carried out using the red LED with the radiation wavelength of 660 nm. For the visual testing, the color scales were used. The indicator reaction was proposed to be carried out in three modes: without concentration and with concentration of the test solution in 100 and 1000 times on the reaction indicator zone of the paper strip (using the pocket pumping device). By the statistical method, the limit of Pd(II) determination for the visual test method (40, 0.47, 0.042 mg/l) was estimated. The palladium detection limit using the reflectometer (19, 0.22, 0.018 mg/l) for the three modes, respectively, was calculated by 3s criterion. The found values of the limiting concentrations were comparable with the metrological characteristics of the known analysis methods in which solid-phase reagents were used. The trueness of the palladium determinations in technological objects of complex composition and drugs has been proven by the independent methods - atomic emission, spectrophotometric and gravimetric methods of analysis. The value of the relative standard deviation of the determined Pd(II) concentration using the portable reflectometer did not exceed 7%.Keywords: palladium(II), formazan, reagent indicator paper, sorption, reflectometry, visual test analysisDOI: http://dx.doi.org/10.15826/analitika.2020.24.2.007  V.M. Ostrovskaya1, E.A. Reshetnyak2, O.S. Chernyshova3, E.Yu. Bryleva3 1 25 State research institute of the Ministry of Defence of Russian Federation", 10 Molodogvardeyskaya Str., Moscow, 121467, Russian Federation2 V.N. Karazin National University, 4 Svoboda Sq., Kharkiv, 61022, Ukraine3 SSI "Institute for Single Crystals" NAS of Ukraine, 60 Nauky Ave, Kharkiv, 61072, UkraineРеагентная индикаторная бумага РИБ-Pd-Тест на основе 1-фенил-5-(3,4-дигидро-6-метил-4-оксо-3Н-пиримидин-2-ил)-формазан-6-целлюлозы предложена для определения содержания палладия сорбционно-рефлектометрическим и визуально-тестовым методами в объектах сложного состава. Изложена методика синтеза РИБ, указан предполагаемый состав металлокомплекса, образующегося в результате гетерогенной индикаторной реакции при рН = 1.5-2.5, с принудительной координацией палладий : реагент = 1 : 1. При взаимодействии РИБ с ионами палладия(II) желтая индикаторная полоса становилась зеленого цвета разной интенсивности. В выбранных условиях показана высокая селективность обнаружения и определения Pd(II). Рефлектометрические измерения проводили с помощью портативного рефлектометра «Экотест-2040», используя красный светодиод с длиной волны излучения 660 нм; для визуального тестирования применяли цветовые шкалы. Индикаторную реакцию предложено проводить в трех режимах: без концентрирования и с концентрированием исследуемого раствора в 100 и 1000 раз на реакционной индикаторной зоне бумажной полосы (применяя карманное прокачивающее устройство). Статистическим методом оценены значения предела определения Pd(II) для визуально-тестовой методики (40, 0.47, 0.042 мг/л) и по 3s-критерию вычислены значения предела обнаружения палладия с использованием рефлектометра (19, 0.22, 0.018 мг/л) для трех режимов, соответственно. Найденные значения предельных концентраций сопоставимы с метрологическими характеристиками известных методик анализа, в которых применяли твердофазные реагенты. Правильность определений палладия в технологических объектах сложного состава и лекарственных препаратах доказана независимыми методами – атомно-эмиссионным, спектрофотометрическим и гравиметрическим методами анализа. Величина относительного стандартного отклонения определяемой концентрации Pd(II) с использованием портативного рефлектометра не превысила 7 %.Ключевые слова: палладий(II), формазан, реагентная индикаторная бумага, сорбция, рефлектометрия, визуальный тестовый анализDOI: http://dx.doi.org/10.15826/analitika.2020.24.2.00

BRST approach to Lagrangian formulation for mixed-symmetry fermionic higher-spin fields

We construct a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with the corresponding Young tableaux having two rows, on a basis of the BRST approach. Starting with a description of fermionic higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a first-class constraint system. For this purpose, we find auxiliary representations of the constraint subsuperalgebra containing the subsystem of second-class constraints in terms of Verma modules. We propose a universal procedure of constructing gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive fermionic fields of any spin. No off-shell constraints for the fields and gauge parameters are used from the very beginning. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincare-group representation. To illustrate the general construction, we obtain a Lagrangian description of fermionic fields with generalized spin (3/2,1/2) and (3/2,3/2) on a flat background containing the complete set of auxiliary fields and gauge symmetries.Comment: 41 pages, no figures, corrected typos, updated introduction, sections 5, 7.1, 7.2 with examples, conclusion with all basic results unchanged, corrected formulae (3.27), (7.138), (7.140), added dimensional reduction part with formulae (5.34)-(5.48), (7.8)-(7.10), (7.131)-(7.136), (7.143)-(7.164), added Refs. 52, 53, 54, examples for massive fields developed by 2 way