Feynman Diagrams, RNA Folding, and the Transition Polynomial

Wednesday, October 31, 2007 - 1:25pm - 1:40pm
EE/CS 3-180
Yongwu Rong (George Washington University)
Feynman diagrams were introduced by physicists. They arise naturally
in mathematics (from knots and singular knots), and in molecular
biology (from RNA folding). In particular, work of G. Vernizzi, H.
Orland, and A. Zee
has shown that the genus of Feynman diagrams plays an important role
in the prediction of RNA structures.

The transition polynomial for 4-regular graphs was defined by Jaeger to
unify polynomials given by vertex reconfigurations similar to the
skein relations of knots. It is closely related to the Kauffman bracket,
Tutte polynomial, and the Penrose polynomial.

We define a transition polynomial for Feynman diagrams and discuss its
properties. In particular, we show that the genus of a Feynman
diagram is encoded in the transition polynomial. This is joint work
with Kerry Luse.
MSC Code: