  Results obtained in the past for free boson systems at zero and nonzero
temperature are revisited to clarify the physical meaning of current algebra
reducible functionals which are associated to systems with density
fluctuations, leading to observable effects on phase transitions. To use
current algebra as a tool for the formulation of quantum statistical mechanics
amounts to the construction of unitary representations of diffeomorphism
groups. Two mathematical equivalent procedures exist for this purpose. One
searches for quasi-invariant measures on configuration spaces, the other for a
cyclic vector in Hilbert space. Here, one argues that the second approach is
closer to the physical intuition when modelling complex systems. An example of
application of the current algebra methodology to the pairing phenomenon in
two-dimensional fermion systems is discussed.
