Dr Hannabuss 16 lectures HT 2006

Tuesday 5.00

Wednesday 3.00

The creation of a
Bose-Einstein condensate
at JILA, Boulder, Colorado

Lecture Notes*
Interesting links
Problem sheets*
* Accessible only from sites within Oxford University.


When relativity is combined with quantum theory using the Dirac equation particle-antiparticle annihilation can occur and the number of particles is no longer fixed; in order to apply quantum theory to light one must be able to deal with quantum theory of systems with infinite numbers of degrees of freedom..

In many complicated systems, such as the molecules of gas in a container, quantum mechanical uncertainty is compounded by ignorance about other details of the system and requires the tools of quantum statistical mechanics. The extended theory predicts the existence of macroscopic quantum states, the Bose-Einstein condensates, which have recently been observed experimentally.

This course will provide an introduction to all these ideas.


b7 and Section c Further Quantum Theory.


Examples of infinite-dimensional linear systems. Quantization. Waves in a finite region. The Casimir effect. The canonical commutation relations for free linear fields. Fock space. Correlation functions. The canonical anticommutation relations for free fields and fermionic Fock space. Clifford algebras. Symplectic spaces. Bogoliubov transformations. Coherent States. Scattering off a classical current. Simple examples of interacting field theories.

Mixed states, density operators. The example of spin systems. Gibbs states. The KMS property. Partition functions. Bose-Einstein condensation.


Link to Mathematical Institute Home Page
Link to Mathematics at Balliol

This page was last updated
on 3 January 2006
KC Hannabuss