  In this paper we demonstrate, that the light-cone lattice approach for the
Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering
method, admits an appropriate framework for computing the finite volume
form-factors of local operators of the model. In this work we compute the
finite volume diagonal matrix elements of the $U(1)$ conserved current in the
pure soliton sector of the theory. Based on the systematic large volume
expansion of our results, we conjecture an exact expression for the finite
volume expectation values of local operators in pure soliton states. At large
volume in leading order these expectation values have the same form as in
purely elastic scattering theories, but exponentially small corrections differ
from previous Thermodynamic Bethe Ansatz conjectures of purely elastic
scattering theories.
