Thursday, 14:00-16:00 and Friday, 10:00-12:00, ESI lecture hall.
The course will start on October 14, 2004

The Renormalization Group (RG) has its origins in quantum field theory and in statistical mechanics. Over the years it has also been developed into a powerful tool in perturbative and constructive field theory, spectral theory and other branches of analysis.

In this course, I give an introduction to the renormalization group differential equation (RGDE) as a tool to study quantum field theory. After a motivation for this class of problems and the method and an introduction to the basic techniques, I will present perturbative and nonperturbative renormalizability proofs based on the RGDE. The beauty of the method is that it allows for combinatorially very simple (and rigorous) renormalizability proofs, and that on the other hand, the full combinatorial structure of the graphical expansion is generated by the equation in a way that is for fermions suitable for nonperturbative bounds. The applications discussed in the course include the Gross-Neveu model and quantum many-body systems.

Literature:
M. Salmhofer: "Renormalization", Springer, 1999
C. Kopper, "Renormierungstheorie mit Flussgleichungen", Shaker
M. Salmhofer, "Renormalization of phi₆³ using RGDE", Hesselberg Lecture Notes