  Light-front time-ordered amplitudes are investigated in the virtual scalar
meson production process in (1+1) dimensions using the solvable scalar field
theory extended from the conventional Wick-Cutkosky model. There is only one
Compton form factor (CFF) in the (1+1) dimensional computation of the virtual
meson production process, and we compute both the real and imaginary parts of
the CFF for the entire kinematic regions of $Q^2>0$ and $t<0$. We then analyze
the contribution of each and every light-front time-ordered amplitude to the
CFF as a function of $Q^2$ and $t$. In particular, we discuss the significance
of the "cat's ears" contributions for gauge invariance and the validity of the
"handbag dominance" in the formulation of the generalized parton distribution
(GPD) function used typically in the analysis of deeply virtual meson
production processes. We explicitly derive the GPD from the "handbag"
light-front time-ordered amplitudes in the $-t/Q^2<<1$ limit and verify that
the integrations of the GPD over the light-front longitudinal momentum fraction
for the DGLAP and ERBL regions correspond to the valence and nonvalence
contributions of the electromagnetic form factor that we have recently reported
[Phys. Rev. D $\textbf{103}$, 076002 (2021)]. We also discuss the
correspondence of the GPD to the parton distribution function for the analysis
of the deep inelastic lepton-hadron scattering process and the utility of the
new light-front longitudinal spatial variable $\tilde{z}$.
