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

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