Pure Postgraduate Seminar - Tyrone Cutler (Southampton) Seminar

Event details

The mathematics surrounding quantum field theory (QFT) is a rich and complex topic which is often as mysterious as the subject itself. In this expository talk I will briefly introduce some of the basic concepts of perturbative QFT and how they lead to the need for renormalisation. This is the process of juggling infinities - arranging the collection of divergent integrals that arise during calculation so as to be left with a finite end result. The problem is well understood but difficult. Recently Connes and Kreimer proposed a new approach using a combinatorial Hopf algebra defined on the collection of Feynman diagrams. It is remarkable that these simple graphical tools contain so much information. I give a brief introduction to their graph-theoretical properties and construct the Hopf algebra, showing how it leads to a solution of the problem.