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We show how to use a worldline-instanton formalism to calculate, to leadingorder in the weak-field expansion, the momentum spectrum of nonlinearBreit-Wheeler pair production in fields that depend on time and one spatialcoordinate. We find a nontrivial dependence on the width, $\lambda$, of thephoton wave packet, and the existence of a critical point $\lambda_c$. For$\lambda<\lambda_c$ and a field with one peak, the spectrum has one peak wherethe electron and positron have the same energy. For $\lambda>\lambda_c$ thissplits into two peaks. We calculate a high-energy ($\Omega\gg1$) expansion,which to leading order agrees with the results obtained by replacing thespace-time field with a plane wave and using the well-known Volkov solutions.We also calculate an expansion for $\Omega\sim a_0\gg1$, where the field isstrong enough to significantly bend the trajectories of the fermions despite$\Omega\gg1$.

Momentum spectrum of nonlinear Breit-Wheeler pair production in space-time fields