  In this work, we show that, for the $i\phi^{3}$ scalar field theory, their
exists a contradiction between the assumption that the field is real and the
fact that the quantized as well as the classical fields have to satisfy the
Klein-Gordon equation. In solving the Klein-Gordon equation for the theory
under investigation, we realized that the field is a pure imaginary solitary
wave which spoils out the non-Hermiticity of the theory. Thus, instead of being
non-Hermitian, the $i\phi^{3}$ scalar field theory is a kind of a
Hermitian-Lee-Wick theory which suffers from the existence of the famous ghost
states and instability problems. We applied a Canonical transformation to
obtain a Non-Hermitian and non-$\mathcal{PT}$-symmetric representation which
leads to the invalidity of the previous trials in the literature to cure the
ghost states problem. Moreover, the solitonic solution is a non-topological one
which is a very strange result to appear for a one component field theory. To
account for this strange result, we conjecture that the $i\phi^{3}$ scalar
field theory has an equivalent Hermitian and non-Lee wick theory that have a
conserved Noether current.
