Quantum field theory

---

Prerequisites

Non-relativistic quantum mechanics, Classical electromagnetism, Special relativity

Useful links

QFT references

transparencies from a summer school

Contents

1. Maxwell's equations in relativistic form

annotated transparencies

2. The lagrangian of Electrodynamics and Noether's theorem

notes

note on the Euler-Lagrange equation for the electromagnetic field

3. Symmetries, Noether theorem, Hamiltonian

notes

4. Problems QFT 1

solutions 1-5

5. Poisson Brackets and canonical quantization

notes

6. Second quantization, microcausality

notes 2020; notes 2021(a) notes 2021(b)

7. Problems QFT 2

notes

8&9. Spin and the Lorentz group I

notes 1; notes 2

10. Propagators, quantization of the Dirac field, quantization of the Maxwell field

notes 2021-fermion quantization and problems with photons

notes on propagators and on the solutions to the Dirac equation
notes on Fermion quantization and on photon quantization
notes on photon quantization and the photon propagator

11. Problems QFT 3

notes
recording

12. Fermion and photon propagators. Interaction lagrangians and renormalisability. The concept of the S Matrix. Link with cross sections.

notes recording Transparencies
[math]\displaystyle{ 2\to 2 }[/math] cross sections

13. Evaluation of the matrix elements of T. Wick's theorem and Feynman rules.

Wick's theorem
notes 2020

14. Problems QFT 4

notes-2021
notes-2020

15. Explicit example [math]\displaystyle{ e^- \mu^-\rightarrow e^-\mu^- }[/math]

notes 2020

16. QED Feynman rules, and the Rutherford cross section [math]\displaystyle{ \sigma(e^- \mu^-\rightarrow e^-\mu^-) }[/math]

notes 2021
notes 2020

17. Problems QFT 5

notes 2021
notes 2020

19. The Compton cross section and related processes

notes

20. Problems QFT 6

notes 2020 part 1
notes 2020 part 2
notes 2021
recording 2021

Exam questions - theory