Quantum Field Theory - Material for the year 2020-2021

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2020-2021
External Lecturer(s): 
Prof. John Wheater
General Prerequisites: 

The course is on QFT, not on its precursors. To help you make sure that you are prepared there will be some preliminary material available on the Course Materials tab.

Course Term: 
Michaelmas
Course Weight: 
1.50 unit(s)

Assessment type:

Course Overview: 

24 lectures
Areas: PT, CMT, Astro, foundational course.
Sequels: Advanced Quantum Field Theory for Particle Physics (HT), Conformal Field Theory (TT),
Quantum Field Theory in Curved Space-Time (TT).

Link to submit your homework (this is not a homework completion course but you still submit your work online)
Click on the relevant link depending on who your Teaching Assistant is:
Federico Buccioni's class: https://cloud.maths.ox.ac.uk/index.php/s/wxMLPpFjzfQ8SeC
Giacomo Marocco's class: https://cloud.maths.ox.ac.uk/index.php/s/aEpTWfCR7wNWLoR
Rok Medves' class: https://cloud.maths.ox.ac.uk/index.php/s/YQiW9AWgHTRWTF2
Arthur Platschorre's class: https://cloud.maths.ox.ac.uk/index.php/s/MLXZpbsSMyLkG6G
Krishnendu Ray's Class:https://cloud.maths.ox.ac.uk/index.php/s/j7ck8HbRm2JBpBp
Aleksandra Ziolkowska's class: https://cloud.maths.ox.ac.uk/index.php/s/zT6HAKK6CCwkJ8p
Deadlines to be confirmed

Course Synopsis: 

The lectures:
Because of the pandemic the lectures will be on-line. They will be pre-recorded and the content of the “blackboards” will be available as a pdf at the same time as the recordings.
We will have timetabled weekly, live, on-line question and answer sessions, and will go through the details of how this will work in the first lecture.
Synopsis
1. Introduction, and Why do we need quantum field theory?
2. Relativistic wave equations
3. Formalism of classical field theory
4. Canonical quantisation of the real scalar field
5. Charge and complex fields
6. Canonical quantisation of the fermion field
7. Interacting fields, formalism and the perturbation expansion
8. Scattering and decay, their relation to amplitudes
9. Calculation of low order Feynman diagrams
10. Regularization, effective and renormalizable QFTs
11. Feynman path integral quantisation

Reading List: 

The classic texts on the subject are by Bjorken and Drell, Relativistic Quantum Mechanics and Relativistic Quantum Fields. Everything in the first is worth knowing; the second is somewhat outdated but still worth a look.
There are many good modern textbooks on QFT. None of them exactly coincides with this course, as we progress you will have to move around in the books, and they all contain a lot more material than we can cover in a 24-lecture course. You will probably find it useful to look at more than one book. Unfortunately, there is no universally accepted set of conventions in QFT so for clarity we will use those of:
An Introduction to Quantum Field Theory by Peskin and Schroeder. This is a very large book and covers a great many detailed topics. It will certainly see you through the first year of learning QFT though you may find it rather heavy going.
Some other books that are certainly worth looking at:
Quantum Field Theory by Mandl and Shaw is very clear on the fundamentals and is a good place to start, especially if you are daunted by the size of some of the other books;
Quantum Field Theory by Srednicki focusses on the path integral before canonical quantisation, but from a particle physics point of view covers all the bases.
Quantum Field Theory in a Nutshell by Zee covers a vast range of the subject. If you like relatively condensed presentations then you will like this book.
Statistical Physics of Fields by Kardar approaches the topic from the rather different statistical mechanical point of view. If you are planning to work in condensed matter or statistical physics then you should certainly read this book at some point.