2019/2020
Research Seminar "Elementary Introduction to Quantum Field Theory"
Category 'Best Course for New Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Instructors:
Mikhail Skopenkov
Language:
English
ECTS credits:
3
Contact hours:
30
Course Syllabus
Abstract
It turns out that rainbow patterns on soapbubbles and unbelievable laws of motion of electrons can be explained by means of one simple-minded model. It is a game, in which a checker moves on a checkerboard by certain simple rules, and we count the turnings. This `Feynman checkerboard' can explain all phenomena in the world (with a serious proviso) except atomic nuclea and gravitation. No prerequisites in physics are assumed; knowledge of school-level mathematics is sufficient. In particular, the course is accessible for 1st year students. We are going to solve mathematical problems and discuss their physical meaning. As a result, we learn basic ideas of quantum field theory on mathematical level of rigor and algorithmic level of clarity.
Learning Objectives
- To solve basic visual problems in quantum field theory on a mathematical level of rigor and thus will become competent in basic notions, tools, general principles and applications of the theory
Expected Learning Outcomes
- To be able to compute the probability to find electron at a given point under various conditions and to prove general theorems on such probabilities
Course Contents
- Feynman's checkerboard: the simplest model of an electron.Feynman's checkerboard: the simplest model of an electron. Double-slit experiment. Lattice Dirac's equation. Spin. Charge. Mass. Convergence of Feynman's checkerboard to Dirac's theory. Source. Medium. Thin film reflection. Wave propagation.
- Extensions of Feynman's checkerboardExtensions of Feynman's checkerboard. External magnetic field. Spin `precession'. Gauge transformations. Curvature. Charge conservation. Identical particles. Antiparticles. Creation and annihilation of electron-positron pairs. QED
Assessment Elements
- Examwritten. Contributes up to 80 points
- Tests2-4 tests, N minutes each; each contributes up to N/2 points
- Written solutionsAn ideal written solution contributes 8 points. Incomplete solution usually contributes 0 points, in special cases --- 7 points. Written solutions are accepted at most one per two weeks (per student). Recommendations for ideal written solutions. http://www.mccme.ru/circles/oim/home/pism.pdf
- Oral solutionsAn oral solution contributes 1-3 points depending on the problem complexity
- Homework problemsA homework problem added by a student to the conduit contributes 1 point. If the solution is checked, then `1' is replaced by a number from -4 to +4 depending on the problem complexity and how serious the gaps are
- Finding bugsFinding a bug not found before contributes 1 point
Interim Assessment
- Interim assessment (2 module)min { 10, [L/15] }, where the Lagrangian L consists of all the grading elements described in this program
Bibliography
Recommended Core Bibliography
- Maldacena, J. (2014). The symmetry and simplicity of the laws of physics and the Higgs boson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1410.6753
Recommended Additional Bibliography
- Feynman, R. P., & Zee, A. (2006). QED : The Strange Theory of Light and Matter (Vol. Expanded Princeton Science Library ed). Princeton, N.J.: Princeton University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=548659