Кто читает:: Факультет математики

Статус:: Дисциплина общефакультетского пула

Когда читается:: 1, 2 модуль

Преподаватель

Скопенков Михаил Борисович

Full 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 checkerboard
Extensions 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

Exam
written. Contributes up to 80 points
Tests
2-4 tests, N minutes each; each contributes up to N/2 points
Written solutions
An 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 solutions
An oral solution contributes 1-3 points depending on the problem complexity
Homework problems
A 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 bugs
Finding 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

Бакалаврская программа «Математика»

Research Seminar "Elementary Introduction to Quantum Field Theory"