  In this work, we show that the traditional effective field approach can be
applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic
potential. The importance of this work lies in the possibility of its extension
to the more important $\mathcal{PT}$-symmetric quantum field theory while the
other approaches which use complex contours are not willing to be applicable.
We calculated the effective potential of the massless $-x^{4}$ theory as well
as the full spectrum of the theory. Although the calculations are carried out
up to first order in the coupling, the predicted spectrum is very close to the
exact one taken from other works. The most important result of this work is
that the effective potential obtained, which is equivalent to the Gaussian
effective potential, is bounded from below while the classical potential is
bounded from above. This explains the stability of the vacuum of the theory.
The obtained quasi-particle Hamiltonian is non-Hermitian but
$\mathcal{PT}$-symmetric and we showed that the calculation of the metric
operator can go perturbatively. In fact, the calculation of the metric operator
can be done even for higher dimensions (quantum field theory) which, up till
now, can not be calculated in the other approaches either perturbatively or in
a closed form due to the possible appearance of field radicals. Moreover, we
argued that the effective theory is perturbative for the whole range of the
coupling constant and the perturbation series is expected to converge rapidly
(the effective coupling $g_{eff}={1/6}$).
