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This work constructs a well-defined and operational form factor expansion ina model having a massless spectrum of excitations. More precisely, the dynamictwo-point functions in the massless regime of the XXZ spin-1/2 chain areexpressed in terms of properly regularised series of multiple integrals. Theseseries are obtained by taking, in an appropriate way, the thermodynamic limitof the finite volume form factor expansions. The series are structured in wayallowing one to identify directly the contributions to the correlator stemmingfrom the conformal-type excitations on the Fermi surface and those issuing fromthe massive excitations (deep holes, particles and bound states). The obtainedform factor series opens up the possibility of a systematic and exact study ofasymptotic regimes of dynamical correlation functions in the massless regime ofthe XXZ spin $1/2$ chain. Furthermore, the assumptions on the microscopicstructure of the model's Hilbert space that are necessary so as to write downthe series appear to be compatible with any model -- not necessarily integrable-- belonging to the Luttinger liquid universality class. Thus, the presentanalysis provides also the phenomenological structure of form factor expansionsin massless models belonging to this universality class.

On the thermodynamic limit of form factor expansions of dynamical correlation functions in the massless regime of the XXZ spin $1/2$ chain