LeClair-Mussardo series for two-point functions in Integrable QFT

We develop a well-defined spectral representation for two-point functions in relativistic Integrable QFT in finite density situations, valid for space-like separations. The resulting integral series is based on the infinite volume, zero density form factors of the theory, and certain statistical functions related to the distribution of Bethe roots in the finite density background. Our final formulas are checked by comparing them to previous partial results obtained in a low-temperature expansion. It is also show that in the limit of large separations the new integral series factorizes into the product of two LeClair-Mussardo series for one-point functions, thereby satisfying the clustering requirement for the two-point function.