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We present the electromagnetic gauge field interpolation between the instantform and the front form of the relativistic Hamiltonian dynamics and extend ourinterpolation of the scattering amplitude presented in the simple scalar fieldtheory to the case of the electromagnetic gauge field theory with the scalarfermion fields known as the sQED theory. We find that the Coulomb gauge in theinstant form dynamics (IFD) and the light-front gauge in the front formdynamics, or the light-front dynamics (LFD), are naturally linked by theunified general physical gauge that interpolates between these two forms ofdynamics and derive the spin-1 polarization vector for the photon that can begenerally applicable for any interpolation angle. Corresponding photonpropagator for an arbitrary interpolation angle is found and examined in termsof the gauge field polarization and the interpolating time ordering. Usingthese results, we calculate the lowest-order scattering processes for anarbitrary interpolation angle in sQED. We provide an example of breaking thereflection symmetry under the longitudinal boost, $P^z \leftrightarrow -P^z$,for the time-ordered scattering amplitude in any interpolating dynamics exceptthe LFD and clarify the confusion in the prevailing notion of the equivalencebetween the infinite momentum frame (IMF) and the LFD. The particularcorrelation found in our previous analysis of the scattering amplitude in thesimple scalar field theory, coined as the J-shaped correlation, between thetotal momentum of the system and the interpolation angle persists in thepresent analysis of the sQED scattering amplitude. We discuss the singularbehavior of this correlation in conjunction with the zero-mode issue in theLFD.

The Electromagnetic Gauge Field Interpolation between the Instant Form and the Front Form of the Hamiltonian Dynamics