  In present work, a relativistic relation that connects the difference of
interacting and non-interacting integrated two-particle correlation functions
in finite volume to infinite volume scattering phase shift through an integral
is derived. We show that the difference of integrated finite volume correlation
functions converge rapidly to its infinite volume limit as the size of periodic
box is increased. The fast convergence of our proposed formalism is illustrated
by analytic solutions of a contact interaction model, the perturbation theory
calculation, and also Monte Carlo simulation of a complex $\phi^4$ lattice
field theory model.
