Infinite Series Of Diagrams Research Articles

Classification of Heegaard diagrams of genus three

We present a classification of the Heegaard diagram of genus 3 and an example of an infinite series of diagrams, which have the same type modeled on the one-dimensional skeleton of the octahedron.

Three-body Coulomb Green function and the reactions with charged particles at low energies

It has been shown that the inclusion of all possible Coulomb rescatterings of three charged particles in intermediate state results in an infinite series of diagrams which have a pole located at the same place as the pole of the pole diagram. The contribution of the pole terms of such infinite series has explicitly been singled out and summed-up. Renormalization of the pole diagram amplitude due to all the possible Coulomb rescatterings of particles in intermediate state has been found. The result obtained means that the three-body Coulomb Green function entering the expression for the reaction amplitude may be written in the form of the renormalized free Green function plus the residue which behaves as in the case of short-range interactions.