  We present the electromagnetic gauge field interpolation between the instant
form and the front form of the relativistic Hamiltonian dynamics and extend our
interpolation of the scattering amplitude presented in the simple scalar field
theory to the case of the electromagnetic gauge field theory with the scalar
fermion fields known as the sQED theory. We find that the Coulomb gauge in the
instant form dynamics (IFD) and the light-front gauge in the front form
dynamics, or the light-front dynamics (LFD), are naturally linked by the
unified general physical gauge that interpolates between these two forms of
dynamics and derive the spin-1 polarization vector for the photon that can be
generally applicable for any interpolation angle. Corresponding photon
propagator for an arbitrary interpolation angle is found and examined in terms
of the gauge field polarization and the interpolating time ordering. Using
these results, we calculate the lowest-order scattering processes for an
arbitrary interpolation angle in sQED. We provide an example of breaking the
reflection symmetry under the longitudinal boost, $P^z \leftrightarrow -P^z$,
for the time-ordered scattering amplitude in any interpolating dynamics except
the LFD and clarify the confusion in the prevailing notion of the equivalence
between the infinite momentum frame (IMF) and the LFD. The particular
correlation found in our previous analysis of the scattering amplitude in the
simple scalar field theory, coined as the J-shaped correlation, between the
total momentum of the system and the interpolation angle persists in the
present analysis of the sQED scattering amplitude. We discuss the singular
behavior of this correlation in conjunction with the zero-mode issue in the
LFD.
