PHYM013 - Module Description

MODULE TITLE	Quantum Many-Body Theory					CREDIT VALUE	15
MODULE CODE	PHYM013		MODULE CONVENER			Dr E. Mariani

DURATION	TERM	1	2	3	Number Students Taking Module (anticipated)		21
	WEEKS	T1:01-11

DESCRIPTION – summary of the module content (100 words)

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 – 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)

On successful completion of this module you 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 Hartree-Fock 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 many-body problem
discuss and explain the physical consequences of the presence of interactions in correlated systems at low temperatures;

Discipline Specific Skills and Knowledge:

use second-quantisation 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 self-study skills;
use mathematical methods to solve problems.

SYLLABUS PLAN – summary of the structure and academic content of the module

Introduction to Second Quantisation
1. The quantum harmonic oscillator
2. Second quantisation of the electromagnetic field: photons
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
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
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 hours

Guided independent study

128 hours

Placement/study abroad

0 hours

DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS