Room 440, Astronomy-Mathematics Building, NTU

(台灣大學天文數學館 440室)

Feynman Diagrams and Singularities of Configuration Polynomials

Uli Walther (Purdue University)

Abstract:

A Feynman diagram is a graph with some extra decorations. It contains in condensed form the information necessary to describe a particle interaction and the corresponding Feynman integral. This integral involves a polynomial that appears (with some power) as denominator of the integrand. Understanding the singularities of this graph polynomial is crucial for evaluating the integrals (which, apart from their physical nature also exhibit some mysterious connection to number theory).

We discuss a classica, more general, approach via matroids that leads to configuration polynomials. We then discuss the structure of the singular locus of graph and configuration polynomials. This is joint work with Graham Denham and Mathias Schulze. No knowledge of Feynman diagrams

is assumed. The talk is intended to be elementary and suitable for students.