Resummation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>?</mml:mi></mml:math> expansion for nonlinear pair production by an electron in a strong electromagnetic field

We show how to resum the Furry-picture $\ensuremath{\alpha}$ expansion in order take quantum radiation reaction and spin transition into account nonlinear trident process (pulsed) plane-wave background fields. The results are therefore nontrivial functions of both field strength, $eE$, coupling quantized photon field, $\ensuremath{\alpha}={e}^{2}/4\ensuremath{\pi}$. effective parameter, $T$, is times $eE/m\ensuremath{\omega}\ensuremath{\gg}1$, which makes higher orders important. that they can change sign spin-dependent part already at $T&lt;1$, will be experimentally accessible. also present a new resummation method essentially does convergent series what Borel-Pad\'e an asymptotic series.