  We formulate the Collective Quantum Field Theory for three-dimensional
bosonic optical lattices and evaluate its consequences in a mean-field
approximation to two collective fields, proposed by Fred Cooper et al. and in a
lowest-order Variational Perturbation Theory (VPT). It is shown that present
mean-field approximation predicts some essential features of the experimentally
observed dependence of the critical temperature on the coupling strength and a
second - order quantum phase transition.In contrast to a recent prediction for
atomic gases by Fred Cooper et. al., we find no superfluid state with zero
condensate fraction.
