  We study the anomalous density in an ultra-cold trapped bose gas in a
variational framework, for both zero and finite temperature. We show that it is
finite in 1D, while it is logarithmically and linearly divergent in 2D and 3D.
The renormalization that we adopt is more reliable and compatible with the
variational scheme. The main outcome is that the anomalous and non condensate
densities are of the
