Form Factors in $D_n^{(1)}$ Affine Toda Field Theories

TL;DR

This paper derives recursion equations for form factors in $D_n^{(1)}$ affine Toda theories, providing explicit calculations and analyzing symmetry and pole structures to advance understanding of their mathematical properties.

Contribution

It introduces new recursion equations for symmetric polynomials in form factors and explores their derivation from residue equations and S-matrix poles.

Findings

Derived recursion equations for form factors

Explicit calculations for low-particle cases

Analysis of symmetry and pole structures in $D_4^{(1)}$

Abstract

We derive closed recursion equations for the symmetric polynomials occuring in the form factors of $D_n^{(1)}$ affine Toda field theories. These equations follow from kinematical- and bound state residue equations for the full form factor. We also discuss the equations arising from second and third order forward channel poles of the S-matrix. The highly symmetric case of $D_4^{(1)}$ form factors is treated in detail. We calculate explicitly cases with a few particles involved.