Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluonpair production 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) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, dW/d(4)xd(2)p(T), from arbitrary E(a)(t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, dW/d(4)xd(2)p(T). We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives d(n)E(a)(t)/dt(n), where n = 1, 2,..., infinity, and that it has the same functional dependence on the 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) -> E(a)(t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark-gluon plasma at RHIC and LHC.