We develop a form factor approach to the study of dynamical correlation
functions of quantum integrable models in the critical regime. As an example,
we consider the quantum non-linear Schr\"odinger model. We derive
long-distance/long-time asymptotic behavior of various two-point functions of
this model. We also compute edge exponents and amplitudes characterizing the
power-law behavior of dynamical response functions on the particle/hole
excitation thresholds. These last results confirm predictions based on the
non-linear Luttinger liquid method. Our results rely on a first principles
derivation, based on the microscopic analysis of the model, without invoking,
at any stage, some correspondence with a continuous field theory. Furthermore,
our approach only makes use of certain general properties of the model, so that
it should be applicable, with possibly minor modifications, to a wide class of
(not necessarily integrable) gapless one dimensional Hamiltonians.Comment: 33 page
