Energy - Momentum equation amidst EM potentials ?

[Widdekind]

If [math]\vec{p}_{tot} = \gamma m \vec{v} + e \vec{A}[/math], what value of the momentum, [math]\vec{p}_{tot}[/math] or [math]\vec{p}_{conventional}[/math], is used in [math]E^2 = E_0^2 + (c p)^2[/math] ? And, what if there is also an electro-static potential, too ? For small electro-static & electro-dynamic potentials, the formula [math](E - V)^2 = E_0^2 + (\vec{p}_{tot} - e \vec{A})^2[/math] seems to correspond to the classical limit.