  Multiflavour gauge theories of matter systems on a three-dimensional lattice
have recently been widely investigated especially in connection with a possible
symmetry enlargement at a continuous phase transition. Abelian models were
studied both with compact gauge fields and in a mixed formulation in which the
coupling with matter fields is in compact form while the gauge fields
Lagrangian is written in terms of non-compact gauge fields, getting quite
different results. Such a mixed formulation is not permissible for non-Abelian
theories, for which however there exists an entirely non-compact formulation
(in which exact gauge invariance is enforced by help of auxiliary fields), that
for SU(2) was shown to yield in the scaling window a larger physical volume
than Wilson's one. The corresponding U(1) non-compact regularization is derived
in the present work. In both Abelian and SU(2) cases there is only one
auxiliary field which for large mass has a linear coupling with the other
fields and it can be integrated out. The coupling with the auxiliary field
might make the inversion of the fermion matrix easier.
