Spectral expansion for finite temperature two-point functions and clustering

TL;DR

This paper refines the spectral expansion method for finite temperature two-point functions in integrable quantum field theories, correcting previous inaccuracies and validating results through symmetry, numerical comparison, and clustering properties.

Contribution

It revisits and corrects the spectral expansion calculation, providing a more accurate expression for two-particle contributions at finite temperature.

Findings

Corrected spectral expansion formulas for two-particle contributions

Validated results through symmetry and numerical checks

Confirmed cluster property up to the evaluated order

Abstract

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