  We generalized the 't Hooft-Veltman method of unitary regulators to put
forward a path-integral framework for finite, alternative theories to a given
quantum field theory. And we demonstrated that the proposed framework is
feasible by providing a finite alternative to the quantum field theory of a
single, self-interacting real scalar field. Here we give two properties of
self-energy that make the corresponding scattering matrix unitary. We show that
the perturbative self-energy has these two properties at least up to the second
order in the coupling constant.
