  A system of two independent Bosonic Harmonic Oscillators is converted into
the respective fourth-order derivative Pais-Uhlenbeck oscillator model. The
conversion procedure displays transparently how the quantization of the
fourth-order derivative Pais-Uhlenbeck oscillator has to be performed in order
not to suffer from the divergence problems of the vacuum state and path
integrals as conjectured most recently by P. D. Mannheim in his article
``Determining the normalization of the quantum field theory vacuum, with
implications for quantum gravity" [arXiv:2301.13029 [hep-th]]. In order to make
the case we present the construction of the path integral, generating
functionals and vacuum persistence amplitudes for PT-symmetry completed systems
in Quantum Mechanics and Quantum Field Theory and discuss some implications to
Quantum Field Theory and Particle Physics.
