## Course curriculum

• 1

### Welcome to the course!

• Welcome to QFT I

• Welcome from your TA Juan

• How to use this course

• Course outline

• Lecture notes

• 2

### Week 1: Introduction, classical field theory, and canonical quantization

• Week 1 Guide

• Natural units

• Scattering of two fast, small objects

• Natural units quiz

• Why quantum field theory?

• Classical field theory

• Klein-Gordon theory

• Distributions

• Noether's theorem

• Canonical quantization

• Classical complex scalar quiz

• Vacuum state

• Casimir effect

• Particles

• Heisenberg picture

• Tutorial 1: Single-particle relativistic propagator and Casimir effect

• Canonical quantization quiz

• If you missed tutorial 1, submit here

• Tutorial 1 Solutions

• Homework 1: Spin and statistics

• 3

### Week 2: Cross sections and LSZ reduction formula

• Week 2 guide

• Trivial scattering

• Cross sections

• Decay rates

• Phase space

• Example: scalar Yukawa cross section

• Cross section and form factor quiz

• Tutorial 2: Complex Klein-Gordon theory, cross sections

• Tutorial 2 solutions

• Homework 2: Muon decay

• Overview: Computing matrix elements

• LSZ reduction formula

• Examining LSZ assumptions

• LSZ and interaction picture quiz

• 4

### Week 3: Dyson's formula, Wick's theorem, propagators, and Feynman diagrams

• Week 3 Guide

• Recap

• Interaction picture

• Dyson's formula

• Wick's theorem

• Wick's theorem quiz

• Propagator

• Tutorial 3: LSZ and interaction picture

• Tutorial 3 solutions

• Feynman diagrams introduction

• Feynman rules for the numerator

• Vacuum diagrams

• Feynman rules for Green's functions

• Feynman diagrams quiz

• 5

### Week 4: Momentum space Feynman diagrams and renormalization

• Week 4 Guide

• Connected versus disconnected diagrams

• Amputation

• Momentum conservation

• Feynman rules for $$i\mathcal{M}$$

• Example: using the Feynman rules

• Feynman diagrams for $$i\mathcal{M}$$ quiz

• Tutorial 4: Feynman diagrams

• Tutorial 4 solutions - 3 (e) solution corrected (Thanks Hikari and others!)

• Homework 3: Feynman diagrams

• Introduction to renormalization

• One point function

• Computing the integral with Wick rotation and Pauli-Villars regularization

• Propagator introduction

• Kallen-Lehmann spectral representation

• Propagator at all orders

• Vertex

• Renormalization quiz

• 6

### Week 5 Renormalization Group

• Week 5 Guide

• Renormalization group introduction

• Euclidean $$\varphi^4$$ theory

• Mass renormalization

• Vertex renormalization

• Running coupling

• Future directions

• Renormalization group quiz

• Tutorial 5: Renormalization

• Tutorial 5 solutions

• Homework 4: Renormalization