We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field Ea(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,
, from arbitrary Ea(t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate,
. We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives
, where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [Ea(t)Ea(t)] and [dabcEa(t)Eb(t)Ec(t)]2, as the constant chromo-electric field Ea result with the replacement: Ea→Ea(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.
11.15.-q 11.15.Me 12.38.Cy 11.15.Tk
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