Module code: MATM054

Module Overview

This module introduces the basic concepts and techniques of the Quantum Theory of Fields.

Module provider


Module Leader


Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 7

JACs code: F342

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

MAT3039 or PHY3044

Module content

Topics covered will include some or all of:

1 Preliminaries (1.5 weeks)

Summary of electromagnetism, without and with 4-vectors
Summary of relativistic invariance
Reminder of quantum harmonic oscillator. Second quantisation
The need for fields

2 Classical Fields (2.5 weeks)

Summary of Lagrangian and Hamiltonian, application to fields
Summary of Noether theorem and symmetries
Examples (real and complex scalars, vectors)
The Klein-Gordon equation
Spinorial representations of the Lorentz group

3 Canonical quantisation of free fields (2 weeks)

The real scalar field 
Fock space
Green functions, retarded/advanced propagators
Locality, causality

4 Interacting fields (2 weeks)

Perturbation theory of phi^4 
Wick's theorem
Feynman graphs and rules
Scattering: S-matrix, LSZ formula, Mandelstam variables, Fermi Golden rule
Infinities and renormalisation

5 Quantum electrodynamics (3 weeks)

Bosonic vs Fermionic statistics
Gamma matrices and Clifford algebras
Schroedinger-Pauli Hamiltonian
Dirac equation
CPT and all that
Famous tree-level QED processes
Gauge invariance: from abelian to non-abelian

Students intending to take the module are encouraged to contact the module coordinator at their earliest convenience for an informal discussion and introduction to the structure of the course, and for possible preliminary reading material if they wish to.


Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 80
School-timetabled exam/test CLASS TEST AND ASSESSED COURSEWORK (50 MINS) 20

Alternative Assessment


Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

Understanding of and ability to interpret and manipulate mathematical statements.

Subject knowledge through the recall of key postulates, theorems and their proofs.

Analytical ability through the solution of unseen problems in the exam and the analysis of slightly more advanced topics in the project.


Thus, the summative assessment for this module consists of:

One two-hour examination (three out of four best answers contribute to the exam mark) at the end of the Semester; worth 80% of the module mark.

One one-hour in-semester test; worth 20% of the module mark.


Formative assessment and feedback

Students receive written feedback via a mid-Semester un-assessed coursework assignment. Students are encouraged to arrange meetings with the module coordinator for questions and verbal feedback on the weekly comprehension of the material throughout the entire duration of the course.


Module aims

  • Introduce students to the mathematical description of relativistic quantum mechanics.
  • Enable students to understand the foundations and basic tools of quantum field theory and their applications to the physical world.
  • Illustrate standard applications of the theory of quantum fields.

Learning outcomes

Attributes Developed
001 Have a firm understanding of the concepts, theorems and techniques of the quantum theory of fields. KC
002 Have a clear understanding of how to apply the mathematical techniques to concrete physical examples (simple scattering processes between elementary particles, symmetry analysis of specific quantum field theories, spinorial calculus and the Dirac equation). KT
003 Be able to explicitly derive the Feynman rules for simple toy-model systems. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Overall student workload

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

A detailed introduction to the relevant theory and its tenets, and to the appropriate mathematical tools for their implementation

Experience (through demonstration) of the methods used to interpret, understand and solve concrete problems, especially for simple toy-model examples


The learning and teaching methods include:


3 x 1 hour lectures per week x 11 weeks, with black/whiteboard written notes to supplement the module notes and question/answer opportunities for students.

Support during the preparation of the mini group-project report and presentation.


A complete set of self-contained notes will be provided in advance to any topics to be treated.


Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list


Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics MSc 2 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MPhys 2 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MMath 2 Optional A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2018/9 academic year.