  Bose atoms in optical lattices are considered at low temperatures and weak
interactions, when Bose-Einstein condensate is formed. A self-consistent
approach, based on the use of a representative statistical ensemble, is
employed, ensuring a gapless spectrum of collective excitations and the
validity of conservation laws. In order to show that the approach is applicable
to both weak and tight binding, the problem is treated in the Bloch as well as
in the Wannier representations. Both these ways result in similar expressions
that are compared for the self-consistent Hartree-Fock-Bogolubov approximation.
A convenient general formula for the superfluid fraction of atoms in an optical
lattice is derived.
