Quantum Field Theory Group, University Jena

Quantum Field Theory

The quantum theory of fields plays a very important role in modern Theoretical Physics. In the Standard Model of Elementary Particles matter is described by bosonic or fermionic fields. Furthermore there are four types of fundamental interactions, which are formulated as gauge field theories. The quantum versions of three of them (electromagnetic, weak and strong interaction) have been well established during the last decades. Together they form the gauge group SU(2)*U(1)*SU(3) and can explain most of the experiments done at high energy laboratories.

Beside these big successes there are still some deep problems in understanding quantum field theories. The perhaps most fascinating is the phenomenon of confinement. It states that quarks which are fundamental 'colored' particles have never been observed freely. On the other hand they occur in deep inelastic scattering processes as constituents of all mesons and baryons. Nowadays it is believed that this fact is due to non-perturbative effects. At low energies the coupling constant of the strong interaction is not small, thus perturbation theory is not valid. Other candidates for non-perturbative effects are the breaking of chiral symmetry, the elektroweak phase transition and violation of baryon number conservation.

The main project of our group is the non-perturbative investigation of quantum field theories. As an infrared cut-off we usually choose the torus. In Yang Mills theories the problem of gauge fixing has to be considered very carefully.

Another long-standing and very interesting topic is the unification of all fundamental forces, sometimes referred to as the 'Theory of Everything'. So far a consistent quantum theory of gravity does not exist. The gravitational interaction between particles is negligible at present day energies. But astronomical observations could give hints for such a theory.

Part of our work deals with quantum field theory at finite temperature and in curved space-time. It is the frame for understanding physical effects like Hawking radiation and phase transitions in the early universe.