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Regular version of the site
Master 2019/2020

Research Seminar of Master’s Programme 1

Type: Compulsory course (Mathematics and Mathematical Physics)
Area of studies: Mathematics
When: 2 year, 1, 2 module
Mode of studies: offline
Master’s programme: Mathematics and Mathematical Physics
Language: English
ECTS credits: 3

Course Syllabus

Abstract

This discipline belongs to the cycle of disciplines of theoretical education and the block of elective disciplines. The study of this discipline is based on the following disciplines: • basic courses in algebra and mathematical analysis; • course of the theory of dynamical systems; • courses of Hamiltonian mechanics and classical field theory; • partial differential equations course; • course of foundations of quantum mechanics
Learning Objectives

Learning Objectives

  • Acquitance the students with the most important physical principles and models, research methods and mathematical structures of modern theoretical and mathematical physics
  • Experiencing with the algebraic and analytical machinery of modern mathematics, development of physical intuition and problem-solving skills, as well as the construction and study of mathematical models of physical phenomena
Expected Learning Outcomes

Expected Learning Outcomes

  • understanding of the basic physical principles and mathematical models, become proficient in the mathematical technique used for the analysis of such models, including methods of representation theory and integrable systems, the technique of generalized functions, functional integration, methods of string theory and gauge theories
  • possessing the skills of independent analysis of mathematical problems, show readiness for a creative approach in the implementation of scientific and technical problems, based on the systematic updating of acquired knowledge, skills and abilities and the use of the latest achievements in the field of mathematical physics; improvement of skills in scientific discussions and presentations at scientific seminars
Course Contents

Course Contents

  • Classical mechanical and field systems with constraints in the Lagrangian and Hamiltonian approaches. Dirac brackets
  • Gauge field theories, their quantization in the formalism of continual integration. Ghosts of Faddeev-Popov
  • BRST-quantization. The Batalin-Vilkovysky-Fradkin formalism
Assessment Elements

Assessment Elements

  • non-blocking Homework
  • non-blocking Talk
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.6 * Exam + 0.2 * Homework + 0.2 * Talk
Bibliography

Bibliography

Recommended Core Bibliography

  • Reed, M. (1972). Methods of Modern Mathematical Physics : Functional Analysis. Oxford: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=567963

Recommended Additional Bibliography

  • Dubrovin, B. (1994). Geometry of 2d topological field theories. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.hep-th%2f9407018