Pair production via crossed lasers

We discuss the intrinsically nonperturbative probability $P_0$ for electron-positron production in the overlap region of a pair of high-intensity lasers, by adapting the Fradkin representation for the logarithm of the fermion determinant to several models defined as approximations to the exact problem. In each case we find for $P_0$ an expression resembling Schwinger’s 1951 expression for the vacuum persistence probability of pair production in an external electric field, proportional to an exponential factor that contains an essential singularity, and hence does not admit a perturbative expansion about zero coupling. Qualitative estimates of the best of these models suggest that realistic yields for $e^{+}{e}^{-}$ production must await lasers of intensity ${10}^{29}\hspace{0.5em}{\mathrm{W}/\mathrm{m}}^2,$ roughly seven orders of magnitude more powerful than the highest intensity of currently known lasers. We comment on the possibility of producing a quark-antiquark pair in this way, and note the possibility of achieving temporary, but large separations of the produced $q-\overline{q}.$