Integrable Quantum Field Theory

Quantum field theory is the application of quantum mechanics to fields and constitutes one of the corner stones of modern theoretical physics. Non-relativistic quantum field theory is the theoretical framework extensively used in condensed matter physics, whereas its relativistic variant is important in the context of particle physics. Quantum field theories describe many-particle systems and possess in general a very large number of degrees of freedom. For this reason they can usually not be treated exactly, but instead one has to rely on perturbative methods, which are controlled expansions in some small quantity usually taken to be the coupling constant. One of the challenges and key problems in this field of research has been from the very beginning to find exact, i.e. non-perturbative, methods and schemes in order to overcome the limitations inevitably imposed by perturbation theory.

 

The concept of integrability has turned out to be very powerful for this purpose. For classical systems it has been known for a long time that once a system possesses as many conserved quantities as degrees of freedom, which is integrability in that context, one may use this property to find explicit solutions for various physical quantities of non-linear dynamical systems. In the late seventies these concepts have been extended from classical to quantum systems, where the conserved quantities are in general associated to some symmetries, which may be hidden in some cases. Originally motivated by concrete physical problems these ideas have led to interesting mathematical concepts such as quantum groups in the context of massive integrable quantum field theory and to a deeper understanding of Virasoro algebras in their massless limits, which are usually conformal field theories.

 

Meanwhile many concrete computational methods based on the concept of integrability have been developed especially in the context of integrable quantum field theories in one time and one space dimension. For instance, to compute exact scattering matrices to all orders in perturbation theory has been achieved for numerous concrete theories. Likewise, but technically far more involved, one may also compute so-called form factors, which are matrix elements of local operators between multi-particle states and the vacuum. These objects may then be used  in the computation of correlation functions between various operators, which is the ultimate goal in any quantum field theory as these quantities describe concrete measurable quantities. To complete this task is part of our main interest of research.

 

We part of the European network EUCLID Integrable models and applications:from strings to condensed matter, which is now terminated

 

The 9-th UK meeting on Integrable Models, Conformal Field Theory and Related Topics was recently held at City University


The 6-th international workshop  on Pseudo Hermitian Hamiltonians in Quantum Physics was held in 2007 at City University

 

The people currently working in this field of research are:

 

Our publications in this area from SPIRES  or  Google Scholar

 

 

In case you are interested to do a PhD in this field of research,

you can write directly to A.Fring@city.ac.uk to obtain further

information.