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

To 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.