  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.
