Research Seminar of Master’s Programme 1

2019/2020

Учебный год

ENG

Обучение ведется на английском языке

3

Кредиты

Кто читает:

Факультет математики

Статус:

Курс обязательный

Когда читается:

2-й курс, 1, 2 модуль

Преподаватели

Ильин Антон Сергеевич

Фейгин Евгений Борисович

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

• 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

• 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

• 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

• Homework
• Talk
• Exam

Interim Assessment

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

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