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Particle interactions are changes in the nature, number, or state of several particles, usually at a specific space-time point, underlying dynamics. They are represented by special "field interaction terms" in quantum field theory and normally entail interchanges of energy, momentum, and sundry quantum numbers. They include scattering, and particle creation and annihilation.
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Interaction of charges in gauge
Even in classical field theory calculation, one cannot just substitute $A_0=0$ in the Lagrangian. Before gauge fixing, $A_0$, being non-dynamical Lagrange-multiplier-like variable, imposes with its EO …
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Relativistic many-particle dynamics as a field theory subsector
In more than 2 dimensions, the so-called "no-interaction theorem" of Leutwyler (see this article for a proof) states that naive attempts at constructing $n$-particle classical relativistic dynamics fa …