Study information

Quantum Many-Body Theory - 2024 entry

MODULE TITLEQuantum Many-Body Theory CREDIT VALUE15
MODULE CODEPHYM013 MODULE CONVENERDr Eros Mariani (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated) 21
DESCRIPTION - summary of the module content

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 phenomena 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.

Pre-requisite modules: PHY2024, PHY3051 and PHYM002 or equivalent modules.
Co-requisite modules:  PHYM001 or equivalent module,

AIMS - intentions of the module

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) (see assessment section below for how ILOs will be assessed)
A student who has passed this module should be able to:
 
Module Specific Skills and Knowledge:
1. quantise fields both on a basis and in a continuum;
2. describe both fields and particles in a consistent occupation number representation;
3. use field operators in simple examples;
4. explain the failings of Hartree-Fock theory and the role played by correlation;
5. derive and solve the simple Bogluibov condensate equations on the basis of a macroscopically occupied state;
6. apply quantum field theory techniques to the many-body problem
7. discuss and explain the physical consequences of the presence of interactions in correlated systems at low temperatures;
 
Discipline Specific Skills and Knowledge:
8. use second-quantisation as a tool for solving quantum mechanical problems;
9. discuss physical systems within the framework of various quantum mechanical representations;
 
Personal and Key Transferable / Employment Skills and Knowledge:
10. give qualitative descriptions of complicated theories and systems;
11. develop self-study skills;
12. use mathematical methods to solve problems.
 
SYLLABUS PLAN - summary of the structure and academic content of the module
I. Introduction to Second Quantisation
  1. The quantum harmonic oscillator
  2. Second quantisation of the electromagnetic field: photons
II. 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
III. 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
IV. 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 (given in hours of study time)
Scheduled Learning & Teaching Activities 22 Guided Independent Study 128 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 20 20×1-hour lectures
Scheduled learning and teaching activities 2 2×1-hour problems/revision classes
Guided independent study 30 5×6-hour self-study packages
Guided independent study 16 4×4-hour problem sets
Guided independent study 82 Reading, private study and revision

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Guided self-study 5×6-hour packages (fortnightly) 1-13 Discussion in class
4 × Problems sets 4 hours per set (fortnightly) 1-13
Solutions discussed in problems classes
 

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Final Examination 100 2 hours 30 minutes 1-13 Written, collective feedback via ELE and solutions.

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Final Examination Written examination (100%) 1-13  Referral/deferral period

 

RE-ASSESSMENT NOTES
An original assessment that is based on both examination and coursework, tests, etc., is considered as a single element for the purpose of referral; i.e., the referred mark is based on the referred examination only, discounting all previous marks. In the event that the mark for a referred assessment is lower than that of the original assessment, the original higher mark will be retained.
 
Physics Modules with PHY Codes
Referred examinations will only be available in PHY3064, PHYM004 and those other modules for which the original assessment includes an examination component - this information is given in individual module descriptors.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Supplementary texts:

  • Abrikosov A.A. (1975), Methods of Quantum Field Theory in Statistical Physics, Dover, ISBN 978-0-486-63228-5 (UL: 530.13 ABR)
  • Baym G. (1969), Lectures on Quantum Mechanics, Benjamin/Cummings, ISBN 8-053-0664-1 (UL: 530.12 BAY)
  • Bethe H.A. (1986), Intermediate Quantum Mechanics (3rd edition), Addison-Wesley, ISBN 0-8053-0757-5 (UL: 530.12 BET)
  • Davydov A.S. (1965), Quantum Mechanics, Pergamon Press, ISBN 978-0-080-13143-6 (UL: 530.12)
  • Doniach S. and Sondheimer E.H. (1974), Green's Functions for Solid State Physicists, Benjamin, ISBN 8-0532394-5 (UL: 530.41 DON)
  • Fetter A.L. and Walecka J.D. (2003), Quantum Theory of Many-Particle Systems, Dover, ISBN 978-0-486-42827-7 (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 0-306-41326-4 (UL: 530.144 INK)
  • Pitaevskii L.P. and Lifshitz E.M. (1980), Statistical Physics (Part 2), Butterworth-Heinemann, ISBN 978-0-750-62636-1 (UL: 530.13 LAN)
  • Messiah A. (1981), Quantum Mechanics, Vol. I (12th edition), North Holland, ISBN 978-0-720-40044-1 (UL: 530.12 MES)
  • Messiah A. (1981), Quantum Mechanics, Vol. II (1st edition), North Holland, ISBN 978-0-720-40045-8 (UL: 530.12 MES)
  • Nozieres P. and Pines D. (1999), Theory of Quantum Liquids, Westview Press, ISBN 978-0-738-20229-7 (UL: 530.42 NOZ)
  • Pethick C.J. and Smith H. (2008), Bose-Einstein Condensation in Dilute Gases (2nd edition), Cambridge University Press, ISBN 978-0-521-84651-6 (UL: 530.43 PET)
  • Sakurai J.J. and Napolitano J.J. (2010), Modern Quantum Mechanics (2nd edition), , ISBN 978-0-805-38291-4 (UL: 530.12 SAK)
  • Schrieffer J.R. (1971), Theory of Superconductivity (3rd edition), Westview Press, ISBN 978-0-7-3820120-7 (UL: 537.623 SCH)

 

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES PHY2024, PHY3051, PHYM002
CO-REQUISITE MODULES PHYM001
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Wednesday 13th March 2024 LAST REVISION DATE Tuesday 21st May 2024
KEY WORDS SEARCH Physics; Feynman diagrams; Fields; Green functions; Many-body theory; Particles; Quantum mechanics.

Please note that all modules are subject to change, please get in touch if you have any questions about this module.