The simplicity and easiness of the lowest-order constrained variational (LO
CV) method among the other many-body techniques, persuaded us to use this m
ethod to study a well known and relatively cumbersome problem, compact QED
in 2 + 1 dimensions. Various quantities such as the ground state energy. th
e mean value of the plaquette variable and the photon mass gap are computed
. Finally, we compare our results with those which have been carried out us
ing other many-body theories.