Spectral expansion for finite temperature two-point functions and clustering

Abstract

Recently, the spectral expansion of finite temperature two-point functions in\nintegrable quantum field theories was constructed using a finite volume\nregularization technique and the application of multidimensional residues. In\nthe present work, the original calculation is revisited. By clarifying some\ndetails in the residue evaluations, we find and correct some inaccuracies of\nthe previous result. The final result for contributions involving no more than\ntwo particles in the intermediate states is presented. The result is verified\nby proving a symmetry property which follows from the general structure of the\nspectral expansion, and also by numerical comparison to the discrete finite\nvolume spectral sum. A further consistency check is performed by showing that\nthe expansion satisfies the cluster property up to the order of the evaluation.\n