  Spontaneous symmetry breaking occurs when the underlying laws of a physical
system are symmetric, but the vacuum state chosen by the system is not. The
(3+1)d $\phi^4$ theory is relatively simple compared to other more complex
theories, making it a good starting point for investigating the origin of
non-trivial vacua. The adaptive perturbation method is a technique used to
handle strongly coupled systems. The study of strongly correlated systems is
useful in testing holography. It has been successful in strongly coupled QM and
is being generalized to scalar field theory to analyze the system in the
strong-coupling regime. The unperturbed Hamiltonian does not commute with the
usual number operator. However, the quantized scalar field admits a plane-wave
expansion when acting on the vacuum. While quantizing the scalar field theory,
the field can be expanded into plane-wave modes, making the calculations more
tractable. However, the Lorentz symmetry, which describes how physical laws
remain the same under certain spacetime transformations, might not be manifest
in this approach. The proposed elegant resummation of Feynman diagrams aims to
restore the Lorentz symmetry in the calculations. The results obtained using
this method are compared with numerical solutions for specific values of the
coupling constant $\lambda = 1, 2, 4, 8, 16$. Finally, we find evidence for
quantum triviality, where self-consistency of the theory in the UV requires
$\lambda = 0$. This result implies that the $\phi^4$ theory alone does not
experience SSB, and the $\langle \phi\rangle = 0$ phase is protected under the
RG-flow by a boundary of Gaussian fixed-points.
