  A class of effective field theory called delta-theory, which improves
ultraviolet divergences in quantum field theory, is considered. We focus on a
scalar model with a quartic self-interaction term and construct the delta
theory by applying the so-called delta prescription. We quantize the theory
using field variables that diagonalize the Lagrangian, which include a standard
scalar field and a ghost or negative norm state. As well known, the indefinite
metric may lead to the loss of unitary of the $S$-matrix. We study the optical
theorem and check the validity of the cutting equations for three processes at
one-loop order, and found suppressed violations of unitarity in the delta
coupling parameter of the order of $\xi^4$.
