  Ultracold atoms in optical lattices undergo a quantum phase transition from a
superfluid to a Mott insulator as the lattice potential depth is increased. We
describe an approximate theory of interacting bosons in optical lattices which
provides a qualitative description of both superfluid and insulator states. The
theory is based on a change of variables in which the boson coherent state
amplitude is replaced by an effective potential which promotes phase coherence
between different number states on each lattice site. It is illustrated here by
applying it to uniform and fully frustrated lattice cases, but is simple enough
that it can easily be applied to spatially inhomogeneous lattice systems.
