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Lagrangian Formulation of Massive Fermionic Antisymm etric Field in Anti de Sitter Space // Tomsk State Pedagogical University Bulletin. 2011. Issue 5 (107). P. 23-30

In this article we apply BRST approach to Lagrangian construction for massive fermionic fields in d-dimensional anti de Sitter space. The obtained Lagrangian theory is a reducible gauge model containing, besides the basic field, a number of auxiliary (Stuckelberg) fields and the order of reducibility grows with the value of the rank of the antisymmetric field. We show that one can get rid of all the auxiliary fields and the final Lagrangian for fermionic antisymmetric field is formulated only in terms of basic field.

Keywords: BRST-approach, higher spin field, massive fermionic fields, anti de Sitter space, BRST-operator, Lagrangian, gauge transformation

BRST-BFV APPROACH TO CONSTRUCTION OF LAGRANGIAN FOR MASSIVE BOSONIC ANTISYMMERIC FIELDS IN CURVED SPACE // Tomsk State Pedagogical University Bulletin. 2011. Issue 8 (110). P. 36-37

We apply the BRST-BFV approach to Lagrangian formulation of bosonic totally antisymmetric tensor fields in arbitrary d-dimensional curved space. The obtained theories are reducible gauge models and the order of reducibility grows with the value of the rank of the antisymmetric field.

Keywords: БРСТ-подход, массивные бозонные поля, искривленное пространство, БРСТ-оператор, лагранжиан, калибровочное преобразование

GAUGE INVARIANT APPROACH TO LAGRANGIAN CONSTRUCTION FOR HIGHER SPIN FIELDS // Tomsk State Pedagogical University Bulletin. 2012. Issue 7 (122). P. 26-31

In this article, we consider the gauge invariant approach to Lagrangian construction for higher spin fields. The method is based on BRST-BFV construction, can be applied to construction of Lagrangians both for massive and massless bosonic and fermionic higher spin fields, in Minkowski or AdS spaces, for fields with mixed index symmetry and fields without any algebraic constraints.

Keywords: BRST-approach, higher spin fields, anti-de Sitter (AdS) space, irreducible representations, gauge invariant Lagrangian

TEST AS A METHOD OF CONTROL AND ASSESSMENT OF CURRENT TRAINING PROGRESS // Tomsk State Pedagogical University Bulletin. 2017. Issue 9 (186). P. 132-135

As part of the creation of a fund of assessment tools for the discipline “Mathematical Analysis”, a test on “Indefinite Integral” is developed for monitoring of students’ knowledge. The test materials for full-time students of the profile faculty were placed and tested in the distance learning system “Open Educational Environment of TSPU”. The advantages of testing along with traditional forms of control are discussed. References to guideline documents regulating the content of the discipline, and consequently the content of the tests are listed. In addition, during the study of the discipline the formation of competence elements is proposed. The test discussed in the article is aimed at the development of one of them. Then the basic settings and characteristics of the test are described. It is noted that it is very important to determine correctly the total time for completing the test, judjing from the number of test questions and the estimated time allotted for each question in the test. The evaluation criteria were also defined. Particular attention is paid to various types of test questions, in addition to a brief description, examples of tasks from the test are given as an illustration. The conclusion about the effectiveness for the using of the test as a form of monitoring is made. Further plans for developing tests on other topics are described, with the prospect of including them in a general test for the final control on the discipline.

Keywords: test tasks, indefinite integral, learning outcomes, professional competencies