Periods and Feynman integral

Andrew Harder, Lehigh University

Abstract: Amplitudes are important quantities in quantum field theory that allow one to study the behavior of interacting subatomic particles. They can be written as sums of integrals of many variables called Feynman integrals. Physicists have studied these integrals for many decades. It is well known that the values that appear have a lot of structure, and that they are often related to interesting mathematical quantities. More recently, it has been observed that Feynman integrals can be interpreted as periods in algebraic geometry. This opens the door to applying the toolbox of algebraic geometry to describe the structure of Feynman integrals. I'll talk about how one can use this relationship to show that the integrals attached to an infinite class of planar 2-loop Feynman graphs are built from hyperelliptic and algebraic functions.

Tea and refreshments available at 3:00 p.m. in the Assmus Conference Room (CU 212).