Program Overview
Theory of Fields 1 Program Details
Overview
The Theory of Fields 1 program is designed to extend and supplement the knowledge achieved through the courses Quantum Mechanics, Classical Electrodynamics, and Relativistic Quantum Mechanics. The program focuses on the role of these courses in quantum field theories.
Course Goals
The goal of the course is to provide students with a thorough understanding of advanced methods of theoretical physics, including classical mechanics, classical electrodynamics, statistical physics, and quantum physics.
Learning Outcomes
Upon completing the degree, students will be able to:
- Demonstrate a thorough knowledge of advanced methods of theoretical physics
- Evaluate clearly the orders of magnitude in situations that are physically different but show analogies
- Apply standard methods of mathematical physics, including mathematical analysis and linear algebra
- Develop a personal sense of responsibility, given the free choice of elective/optional courses
- Develop written and oral English language communication skills essential for pursuing a career in physics
- Search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development
Course Description
The course covers the following topics:
- Action, Lagrangian density, Euler-Lagrange equations of motion, momentum density, and Hamiltonian density
- Noether's theorem and examples
- Quantization of the Klein-Gordon field and the Dirac field
- Poincare transformations of coordinates, momenta, and fields
- Various representations of the Poincare symmetry
- Interacting fields, including examples of phi^4 theory, Yukawa theory, and quantum electrodynamics
- Derivation of the Dyson's formula and the Wick's theorem
- Feynman rules for phi^4 theory, Yukawa theory, and quantum electrodynamics
Course Structure
The course consists of 15 weeks of lectures and exercises, covering the following topics:
- Causality and necessity of field theory
- Basics of field theory: action, Lagrangian density, Euler-Lagrange equations of motion, momentum density, and Hamiltonian density
- Quantization of the Klein-Gordon field
- Poincare transformations of coordinates, momenta, and fields
- Various representations of the Poincare symmetry
- Dirac and Weyl equations
- Free-particle solutions in the chiral representation
- Quantization of the Dirac field
- Spin and spin-projectors for the Dirac field
- Interacting fields: examples of phi^4 theory, Yukawa theory, and quantum electrodynamics
- Derivation of the Dyson's formula and the Wick's theorem
- Feynman rules for phi^4 theory in x- and p- space
- S-matrix and asymptotic states
- Formula for evaluation of S-matrix elements in terms of Feynman diagrams
- Feynman rules for quantum electrodynamics
Requirements for Students
Students are required to attend lectures and exercises regularly.
Grading and Assessing the Work of Students
The exam has three parts: solving homework problems, written examination, and oral examination. Part of the written examination points may be achieved through homeworks.
Literature
- M. E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Addison Wesley, 1995
- S. Weinberg, The Quantum Theory of Fields, I, Cambridge, 1995
Prerequisites
- Attended: Elementary Particle Physics 1
- Passed: Elementary Particle Physics 1
Semester
- 7th semester: Regular study - Physics
- 8th semester: Regular study - Physics