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

Recently the paper “Schwinger mechanism for gluon pair production in the presence of arbitrary time dependent chromo-electric field” by G.C. Nayak was published [Eur. Phys. J. C 59:715, 2009 ; arXiv:0708.2430 ]. Its aim is to obtain an exact expression for the probability of non-perturbative gluon pair production per unit time per unit volume and per unit transverse momentum in an arbitrary time-dependent chromo-electric background field. We believe that the obtained expression is open to question. We demonstrate its inconsistency on some well-known examples. We think that this is a consequence of using the so-called “shift theorem” [ arXiv:hep-th/0609192 ] in deriving the expression for the probability. We make some critical comments on the theorem and its applicability to the problem in question.