There is no regular procedure for the calculation of the short-range properties of the correlation functions in interacting quantum theories so far. I will demonstrate, however, how to do that for the Lieb-Liniger model. The discussed approach will relate the short-range and the universal long-range physics through the infinite set of Ward identities stemming from the integrability of the model. As an example, I will present an explicit expression for the three-body local correlation function, measured in a recent experiment. I will discuss the applicability of the approach to other models as well.

Uninersite de Geneve