PHYM013 
Quantum ManyBody Theory 
202223 

Dr E. Mariani 


Delivery Weeks: 
T1:0111 

Level: 
7 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
21 students (approx) 

Description
Starting with the secondquantisation formalism, the module uses sophisticated
methods (Green functions, Feynman diagrams, and relativistic and
nonrelativistic quantum fieldtheories) to analyse the various phaenomonena
that arise from the presence of interactions in manybody quantum systems of
bosons and fermions, including the HartreeFock approximation, the microscopic
Bogoliubov theory of superfluidity, spontaneous symmetrybreaking and the BCS
theory of superconductivity.
Module Aims
The aim of the module is to introduce the foundations of manybody 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 highenergy physics will also be emphasised and
illustrated.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
 quantise fields both on a basis and in a continuum;
 describe both fields and particles in a consistent occupation number representation;
 use field operators in simple examples;
 explain the failings of HartreeFock theory and the role played by correlation;
 derive and solve the simple Bogluibov condensate equations on the basis of a macroscopically occupied state;
 apply quantum field theory techniques to the manybody problem
 discuss and explain the physical consequences of the presence of interactions in correlated systems at low temperatures;

Discipline Specific Skills and Knowledge:
 use secondquantisation as a tool for solving quantum mechanical problems;
 discuss physical systems within the framework of various quantum mechanical representations;

Personal and Key Transferable / Employment Skills and Knowledge:
 give qualitative descriptions of complicated theories and systems;
 develop selfstudy skills;
 use mathematical methods to solve problems.
Syllabus Plan

Introduction to Second Quantisation
 The quantum harmonic oscillator
 Second quantisation of the electromagnetic field: photons

Quantum Field Theory of Interacting Bosons
 Introduction to the quantum field theory formalism for bosons
 Quasiparticles in a system of interacting bosons
 Bogoliubov microscopic theory of superfluidity
 Theory of the condensed states: GrossPitaevski equation

Quantum Field theory of Interacting Fermions
 Introduction to the quantum field theory formalism for fermions
 Quasiparticles in a system of interacting bosons: HartreeFock approximation
 Cooper instability for electrons with attractive interactions
 BCS theory of superconductivity

Introduction to Feynman Diagrams
 Introduction to singleparticle Green's functions at zero temperature
 The FeynmanDyson perturbation theory
 HartreeFock revisited: diagrammatic approach
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
20×1hour lectures 
20 hours

SLT 
2×1hour problems/revision classes 
2 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
4×4hour problem sets 
16 hours

GIS 
Reading, private study and revision 
82 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
113 
Discussion in class 
0% 
4 × Problems sets 
4 hours per set 
Fortnightly 
113 
Solutions discussed in problems classes. 
100% 
Final Examination 
2 hours 30 minutes 
January 
113 
Mark via MyExeter, collective feedback via ELE and solutions. 
Resources
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:

Abrikosov A.A. (1975), Methods of Quantum Field Theory in Statistical Physics, Dover, ISBN 9780486632285 (UL: 530.13 ABR)

Baym G. (1969), Lectures on Quantum Mechanics, Benjamin/Cummings, ISBN 805306641 (UL: 530.12 BAY)

Bethe H.A. (1986), Intermediate Quantum Mechanics (3^{rd} edition), AddisonWesley, ISBN 0805307575 (UL: 530.12 BET)

Davydov A.S. (1965), Quantum Mechanics, Pergamon Press, ISBN 9780080131436 (UL: 530.12)

Doniach S. and Sondheimer E.H. (1974), Green's Funtion for Solid State Physic, Benjamin, ISBN 805323945 (UL: 530.41 DON)

Fetter A.L. and Walecka J.D. (2003), Quantum Theory of ManyParticle Systems, Dover, ISBN 9780486428277 (UL: 530.144 FET)

Feynman R.P., Leighton R.B. and Sands M. (1965), Lectures on Physics, Vol. III, (UL: 530 FEY/X)

Heitler W. (1954), Quantum Theory of Radiation, Clarendon Press (UL: 530.14 HEI)

Inkson J.C. (1984), Many Body Theory of Solids, Plenum, ISBN 0306413264 (UL: 530.144 INK)

Pitaevskii L.P. and Lifshitz E.M. (1980), Statistical Physics (Part 2), ButterworthHeinemann, ISBN 9780750626361 (UL: 530.13 LAN)

Messiah A. (1981), Quantum Mechanics, Vol. I (12^{th} edition), North Holland, ISBN 9780720400441 (UL: 530.12 MES)

Messiah A. (1981), Quantum Mechanics, Vol. II (1^{st} edition), North Holland, ISBN 9780720400458 (UL: 530.12 MES)

Nozieres P. and Pines D. (1999), Theory of Quantum Liquids, Westview Press, ISBN 9780738202297 (UL: 530.42 NOZ)

Pethick C.J. and Smith H. (2008), BoseEinstein Condensation in Dilute Gases (2^{nd} edition), Cambridge University Press, ISBN 9780521846516 (UL: 530.43 PET)

Sakurai J.J. and Napolitano J.J. (2010), Modern Quantum Mechanics (2^{nd} edition), , ISBN 9780805382914 (UL: 530.12 SAK)

Schrieffer J.R. (1971), Theory of Superconductivity (3^{rd} edition), Westview Press, ISBN 9780738201207 (UL: 537.623 SCH)
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Condensed Matter I (PHY2024), Electromagnetism II (PHY3051) and Quantum Mechanics II (PHYM002) 
Corequisite Modules 
Statistical Physics (PHYM001) 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
113 
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% 

Miscellaneous
IoP Accreditation Checklist 
 N/A this is an optional module

Availability 
MPhys only 
Distance learning 
NO 
Keywords 
Physics; Feynman diagrams; Fields; Green functions; Manybody theory; Particles; Quantum mechanics. 
Created 
01Oct11 
Revised 
12Sep13 