  In this paper we present a particle-number-conserving (PNC) functional
formalism to describe the dynamics of a cold bosonic gas. Treating the total
number of particles as a constraint, whereby the phase invariance of the theory
becomes local in time, we study this U(1) gauge theory using DeWitt's "gauge
invariant effective action" techniques. Our functional formulation and earlier
PNC proposals are shown to yield equivalent results to next-to-leading order in
an expansion in the inverse powers of the total number of particles. In this
more general framework we also show that earlier PNC proposals can be seen as
different gauge (and gauge fixing condition) choices within the same physical
theory.
