  This paper considers the issue of Bose-Einstein condensation in a weakly
interacting Bose gas with a fixed total number of particles. We use an old
current algebra formulation of non-relativistic many body systems due to Dashen
and Sharp to show that, at sufficiently low temperatures, a gas of weakly
interacting Bosons displays Off-diagonal Long Range Order in the sense
introduced by Penrose and Onsager. Even though this formulation is somewhat
cumbersome it may demystify many of the standard results in the field for those
uncomfortable with the conventional broken symmetry based approaches. All the
physics presented here is well understood but as far as we know this
perspective, although dating from the 60's and 70's, has not appeared in the
literature. We have attempted to make the presentation as self-contained as
possible in the hope that it will be accessible to the many students interested
in the field.
