Special topics in field theory(Fall semester 1396)
Description of the course

This is a onesemester course on fundamentals of quantum field
theory as mainly used in areas other than high energy physics, like
condensed matter physics, statistical mechanics, quantum information
and the like. Of course it also touches the basic formalism of
relativisitic quantum field theory. It is suitable for students who
need only an elementary introduction to the subject. It is open to all
graduate and undergraduate of physics and mathematics. At the
end of the course, the student is supposed to know only the basic
concepts and techniques of quantum field theory as used in various
areas of theoretical physics. Students who want to study high energy
physics are advised to take the 3
semester Quantum Field Theory course.
Prerequisites

Knowledge of quantum mechanics, and statistical physics is essential.
The students are required to stuy a great deal on their own.
Textbook and weekly schedule
Weekly schedule: Saturday and Monday, 4:306:30 pm, Room 412.
Contents:
Collective excitations, particles and fields,Free scalar field theory, phonons,
Second Quantization and its application in condensed matter physics
Interacting electron gas, Heisenberg Ferro and antiferromagnet, Hubbard Model, Spin waves, Dilute Bose gas,
Bogoluibov Theory, Electron phonon interaction,
Path Integral Methods in quantum mechanics and statistical physics,
Double well potential, Tunneling and instantons, unstable vacuum and bounces, false vacuum, Path integrals for spins,
topological terms in field theory,
Functional Field Theory,
Many body Path integrals, coherent states for bosons and fermions, Field integral for quantum partition function, Weakly
interacting electron gas,
Relativistic Quantum Mechanics
KleinGordon and Dirac Equation, symmatry and covariance, Angular momentum and spin, Charged scalar field, Dirac field,
Introduction to quantum electrodynamics, Introduction to gauge theory, Introduction to the standard model of particle physics (GlashowSalamWeinberg theory).
Lecture notes:
Will be uploaded on a weekly basis:1Classical Mechanics of Particles
2Classical Mechanics of Fields
2a: Symmetry
3Motivations for Quantum Field Theory
4Second Quantization, NonRelativistic Quantum Fields
5Quantization of classical fields, Collective excitations
6Lorentz Group and its representations
7KleinGordon Field
8Dirac Field
9Path integrals in quantum and statistical fields (part I)
10Path integrals in quantum and statistical fields (part II)
11Applications of second quantization in condensed matter physics (part I)
12Applications of second quantization in condensed matter physics (part II)
13Gauge field theory and the standard model
Homeworks:
The problems are included in the lecture notes. You are supposed to solve all of them in order to succeed in the exams.