We describe the simulation of a quantum relativistic wavepacket propagating in electric and magnetic fields. We start from first principles in QED with the intent of exploring the effects of spin, extended wavepackets, and radiation reaction on particle motion. (This initial work neglects radiation reaction and anti-particle effects). In the numerical simulation of wavepackets we use unitary integrators, adapted to particle propagation in a background (though possibly time-dependent) vector potential.
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