PHYM013 Quantum Many-Body Theory 2023-24
Dr E. Mariani
Delivery Weeks: T1:01-11
Level: 7 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 21 students (approx)


Starting with the second-quantisation formalism, the module uses sophisticated methods (Green functions, Feynman diagrams, and relativistic and non-relativistic quantum field-theories) to analyse the various phaenomonena that arise from the presence of interactions in many-body quantum systems of bosons and fermions, including the Hartree-Fock approximation, the microscopic Bogoliubov theory of superfluidity, spontaneous symmetry-breaking and the BCS theory of superconductivity.

Module Aims

The aim of the module is to introduce the foundations of many-body quantum theory, from both the technical and physical points of view. Although many of the examples are drawn from condensed matter physics, the analogies between these and the theories of high-energy physics will also be emphasised and illustrated.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

Syllabus Plan

  1. Introduction to Second Quantisation
    1. The quantum harmonic oscillator
    2. Second quantisation of the electromagnetic field: photons
  2. Quantum Field Theory of Interacting Bosons
    1. Introduction to the quantum field theory formalism for bosons
    2. Quasiparticles in a system of interacting bosons
    3. Bogoliubov microscopic theory of superfluidity
    4. Theory of the condensed states: Gross-Pitaevski equation
  3. Quantum Field theory of Interacting Fermions
    1. Introduction to the quantum field theory formalism for fermions
    2. Quasiparticles in a system of interacting bosons: Hartree-Fock approximation
    3. Cooper instability for electrons with attractive interactions
    4. BCS theory of superconductivity
  4. Introduction to Feynman Diagrams
    1. Introduction to single-particle Green's functions at zero temperature
    2. The Feynman-Dyson perturbation theory
    3. Hartree-Fock revisited: diagrammatic approach

Learning and Teaching

Learning Activities and Teaching Methods

Description Study time KIS type
20×1-hour lectures 20 hours SLT
2×1-hour problems/revision classes 2 hours SLT
5×6-hour self-study packages 30 hours GIS
4×4-hour problem sets 16 hours GIS
Reading, private study and revision 82 hours GIS


Weight Form Size When ILOS assessed Feedback
0% Guided self-study 5×6-hour packages Fortnightly 1-13 Discussion in class
0% 4 × Problems sets 4 hours per set Fortnightly 1-13 Solutions discussed in problems classes.
100% Final Examination 2 hours 30 minutes January 1-13 Mark via MyExeter, collective feedback via ELE and solutions.


The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

Supplementary texts:


Further Information

Prior Knowledge Requirements

Pre-requisite Modules Condensed Matter I (PHY2024), Electromagnetism II (PHY3051) and Quantum Mechanics II (PHYM002)
Co-requisite Modules Statistical Physics (PHYM001)


Re-assessment is not available except when required by referral or deferral.

Original form of assessment Form of re-assessment ILOs re-assessed Time scale for re-assessment
Whole module Written examination (100%) 1-13 August/September assessment period

Notes: See Physics Assessment Conventions.

KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 22 hrs
GIS - guided independent study 128 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 0%
Written exams 100%
Practical exams 0%
Total 100%


IoP Accreditation Checklist
  • N/A this is an optional module
Availability MPhys only
Distance learning NO
Keywords Physics; Feynman diagrams; Fields; Green functions; Many-body theory; Particles; Quantum mechanics.
Created 01-Oct-11
Revised 12-Sep-13