A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the quantum transfer matrix of the model. The $n$th summand of the series is a multiple integral accounting for all $n$-particle $n$-hole excitations of the quantum transfer matrix. In previous works the expressions for the form factor amplitudes appearing under the integrals were either again represented as multiple integrals or in terms of Fredholm determinants. Here we obtain a representation which reduces, in the zero-temperature limit, essentially to a product of two determinants of finite matrices whose entries are known special functions. This will facilitate the further analysis of the correlation function.
Comment: 61 pages, v2: typos corrected, discussion extended, references added and updated, version to appear in J. Math. Phys, v3: a few typos corrected