Schwinger Mechanism for Quark-Antiquark Production in the Presence of Arbitrary Time Dependent Chromo-Electric Field

We study the Schwinger mechanism in QCD in the presence of an arbitrary time-dependent chromo-electric background field $E^a(t)$ with arbitrary color index $a$=1,2,…8 in SU(3). We obtain an exact result for the non-perturbative quark (antiquark) production from an arbitrary $E^a(t)$ by directly evaluating the path integral. We find that the exact result is independent of all the time derivatives $\frac{d^n{E}^a(t)}{d{t}^n}$ where $n=1,2,\mathrm{.}\mathrm{.}\mathrm{.}\mathrm{\infty }$. This result has the same functional dependence on two Casimir invariants $[E^a(t)E^a(t)]$ and $[d_{abc}{E}^a(t)E^b(t)E^c(t){]}^2$ as the constant chromo-electric field $E^a$ result with the replacement: $E^a\to E^a(t)$. This result relies crucially on the validity of the shift conjecture, which has not yet been established.