## Course curriculum

• 1

### Extra completely optional references

• Discussion on one point function of A_\mu after Friday Q and A

• operator gauge symmetry of QED

• Representations of the Lorentz group

• Tutorial to derive Lie algebra of the Lorentz group

• Tutorial solution for Lie algebra of the Lorentz group

• Is the particle created by b or c really spin 1/2? (tutorial)

• spin 1/2 tutorial solution

• spin statistics theorem by Pauli

• 2

### Dirac's equation and solutions; Weyl and Majorana spinors

• Review quiz for the Dirac equation

• The Dirac equation

• Hamiltonian of the Dirac theory

• Physics Joke: a fishing story

• Review quiz for covariantness of the Dirac equation

• The covariantness of the Dirac equation

• Review quiz for Dirac field has spin half

• The Dirac field has spin half

• After lesson quiz: Notice this quiz is longer than usual.

• We recommend to charge onwards for two more lessons. Otherwise make sure to review the last quiz before starting next lessons.

• Weyl spinor

• Completely optional: Weyl spinor in condensed matter physics

• Majorana spinor

• Completely optional: Majorana spinor in condensed matter physics

• Tutorial one: Dirac, Majorana and Weyl spinors

• Tutorial one solution

• Completely optional: a proof that helicity (massless) is Lorentz invariant.

• Completely optional: reference for two component spinor

• Quiz before solutions of the Dirac equations

• Solutions of the Dirac equations

• 3

### Welcome to the course!

• Course requirement

• Motivation

• Outline and convention

• Learning objectives

• Acknowledgement

• Lecture Notes

• 4

### Dirac's Lagrangian

• Dirac's Lagrangian

• After lesson quiz for Dirac's Lagrangian

• Homework one

• Questions and comments (Week 1) ?

• 5

### Symmetries of Dirac's Lagrangian

• The Weyl Lagrangian

• The definition of parity

• Story: the discovery of parity violation in nature (youtube video).

• Activity: the effect of a mirror on right-handed spinor

• Quiz for activity

• Spinor bilinears

• Quiz before global and gauge symmetry

• global symmetry and gauge the global symmetry

• 6

### Quantization of the Dirac theory

• Review quiz before quantization of Dirac theory

• Quantization of the Dirac theory

• quiz before states

• States

• quiz before anti-particle and Heisenbert picture

• anti-particle and Heisenberg picture

• Causality

• Tutorial two

• Tutorial two solution

• Homework Two

• Questions and Comments (Week 2)?

• 7

### Interacting with fermions

• Updated lecture notes (Nika (Thanks!) found an error around equation 214 and I found some in the later chapters)

• Interview questions for first two weeks

• long quiz before review of the scalar case

• An overview and then a review of the scalar case

• A story from Gang

• Fermionic LSZ formula

• Before quiz on wick theorem

• Dyson formula and Wick theorem

• 8

### Yukawa theory and Feynman rules

• Before quiz for Yukawa theory

• Scattering amplitudes and Feynman rules for Yukawa theory

• In class exercise

• Scattering amplitudes and Feynman rules for Yukawa theory, continued

• Tutorial three: the Feynman Rules

• Tutorial three solution

• Summary: Yukawa Feynman rules; minus signs

• Questions and Comments (Week 3)?

• 9

### Quantizing Maxwell theory

• before quiz for Maxwell theory

• Classical Maxwell theory

• Quantization of Maxwell theory

• 10

### Quantum Electrodynamics at tree level

• Two scattering processes for QED

• 30 mins before tutorial four

• Tutorial Four

• Tutorial Four Solution

• List of Feynman Rules is always handy. Yes you can use it for interview too.

• The Rubric for Feynman diagrams and matrix element

• The Project (Debriefing)

• The Project (The excecution)

• The Project (Teams and submit here)

• The complete interview questions (note the third/last homework is NOT interviewed)

• Homework Three (Last Homework)

• Two little excercises for homework three: I suggest you do it when you start the homework

• The companion video for homework three: I suggest you watch it when you start your homework.

• Questions and Comments (Week 4)?

• 11

### Renormalization of QED

• Interview Schedule

• Superficial degree of divergence

• After quiz for superficial degree of divergence

• Renormalization of QED: the electron self energy

• Tutorial Five

• Tutorial five solution

• Questions and Comments (Week 5)?