  This work studies the relationship between gauge-invariant and non
gauge-invariant abelian vector models. Following a technique introduced by
Harada and Tsutsui, we show that the Proca and the Chiral Schwinger models may
both be viewed as gauge-fixed versions of genuinely gauge- invariant models.
This leads to the proposal that any consistent Abelian vector model with no
gauge symmetry can be understood as a gauge theory that had its gauge fixed,
which establishes an equivalence between gauge-invariant and non
gauge-invariant models. Finally, we show that a gauge-invariant version of the
chiral Schwinger model, after integrating out the fermionic degrees of freedom,
can be identified with the two-dimensional Stueckelberg model without the gauge
fixing term.
