A picture’s worth a thousand symbols

Feynman diagrams provide a pictorial representation of complicated mathematical calculations involved in the physics of particle interactions. These pictures have a fairly simple heuristic interpretation which can be roughly understood by non-experts. In addition to providing a shorthand representation for complex mathematical expressions, however, Feynman diagrams can also be manipulated in order to determine relationships between expressions involving  Feynman diagrams. An example of this approach involves cutting rules which specify the relevant diagrams for determining production rates of particles in high energy collisions. Cutting rules have been understood and applied for some time in calculating particle production rates in zero temperature (ie. vacuum) field theory. Cutting rules in finite-temperature (ie. in a medium) field theory are somewhat more complicated and have not yet been proven. We are currently in the process of a general proof of  finite temperature cutting rules.    In this talk I hope to give the audience a basic understanding of Feynman diagrams and their applications, and cutting rules in finite temperature field theory.