We discuss the intrinsically nonperturbative probability P-0 for electron-p
ositron production in the overlap region of a pair of high-intensity lasers
, by adapting the Fradkin representation for the logarithm of the fermion d
eterminant to several models defined as approximations to the exact problem
. In each case we find for P-0 an expression resembling Schwinger's 1951 ex
pression for the vacuum persistence probability of pair production in an ex
ternal 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 sug
gest that realistic yields for e(+)e(-) production must await lasers of int
ensity 10(29) W/m(2), roughly seven orders of magnitude more powerful than
the highest intensity of currently known lasers. We comment on the possibil
ity of producing a quark-antiquark pair in this way, and note the possibili
ty of achieving temporary, but large separations of the produced q-(q) over
bar.