Discipline: 
Mathematics
Status: 
Available
Level: 
PhD Project
Level: 
Masters Project

Analytic computation of correlation functions is a very challenging problem in the theory of exactly soluble models in condensed matter physics and integrable quantum field theories. There is much interest in this field internationally leading to high-profile research activity at present. A key part of this project is to evaluate correlation functions and form factors of physical significance. The recent development of sophisticated algebraic and analytic methods makes the computation of such correlators feasible.
A great success in the understanding of physical phenomena such as phase transitions in quantum systems has come through the study of exactly soluble models. As is well known most problems of physical interest are of a non-perturbative and non-linear nature and therefore are very difficult to solve. Under proper approximations these complex physical problems reduce to less complex but physically non-trivial models that can be solved exactly. Such exactly soluble models inherit many physical features of and therefore provide important insight into the original systems. One of the consequences of such approximations is that form factors and correlation functions can be computed in closed form so providing essential information for the full description of the original systems.
This project is to capitalize on our recent success in the evaluation of correlators of some soluble models by undertaking a through and systematic investigation into the algebraic formulation of correlation functions and form factors. This is to be achieved by further developing the vertex operator method as well as the factorizing F-matrix method. The latter approach will enable correlation functions and form factors to be expressed in determinant representations.