qftforgiftedamateur     qftinanuttshell

Course outline: The outline can be downloaded here.

Class timings: 10:30 to 11:45 am, Monday and Wednesday, Room: 202  SSE Complex.

Marking scheme: Homeworks 40%, Midterm 30%, Final 30%

Pre-mid term

sdTo access the video recording, click on the numbered links below.

Introduction to Quantum Field Theory: Prerequisites

1: Overview and Special Relativity (Lecture 1)

  • Overview
  • 4-Vectors, Minkowski space
  • Lorentz transformation, Lorentz boost
  • Natural units vs relativistic units
  • Space time diagrams, Simultaneity
  • Lorentz invariants

2: Special Relativity and Classical Mechanics (Lecture 2)

  • Special relativity: 4-velocity
  • Mechanics of relativistic particles
  • Final momentum from langrangian
  • Energy of the system: Hamiltonian
  • Minkowski tensor and inner product

3: Classical Field Theory (Lecture 3)

  • Simple concept of field
  • Example of a single particle
  • Non-relativistic particle equation
  • Basic principles of field theory
  • Klein-Gordon equation
  • Solution to Klein-Gordon equation
  • Particles inside two interacting scalar fields

Homework 1: Hw1 (pdf) (Due date: 6 February, 2018 10:00 am) Solution: Solution 1 (pdf)

4: Lagrangian Formulation of Electromagnetism (Lecture 4)

Homework 2: HW2 (pdf) (Due date: 15 February, 2018 04:00 pm) Solution: Solution 2 (pdf)

5: Electromagnetic Field Tensors (Lecture 5)

  • Electric field components
  • EM field tensor
  • Maxwell’s equations (homogeneous and in homogeneous)
  • Locality principle
  • Lorentz co-variant form of in homogeneous Maxwell’s equations
  • Gauge invariance

Homework 3: HW3 (pdf) (Due date: 19 February, 2018 04:00 pm) Solution: Solution 3 (pdf)


Introduction to Quantum Field Theory: Second Quantization

6: Noether’s Theorem, Second Quantization (Lecture 6)

  • Derivation, Noether’s current, Noether’s momentum
  • Energy momentum tensor
  • Uncoupled and Coupled harmonic oscillators
  • Second quantization

7: Second Quantization continued: Quantization of Operators (Lecture 7)

  • Occupation number
  • Continuum limit
  • Field operators
  • Second quantization of single particle operators
  • Examples

Homework 4: HW4 (pdf) (Due date: 26 February, 2018 04:00 pm)

8: Examples of Second Quantization (Lecture 8)

  • Second quantized form of Hamiltonian (in position and momentum space)
  • Interaction (2 – particles) – Feynman diagram
  • Magnetic interactions (String operators, Jordan-Wigner transformations)
  • Further examples – Magnons, Tight binding model, Hubbard model.