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The simplicity and easiness of lowest order constrained
variational, (LOCV), method among the other many body techniques,
persuade us to use this method for studying a well known and
relatively cumbersome problem, the compact QED in 2+1 dimensions.
Various quantities such as the ground state energy, mean value of
plaquette variable and photon mass gap are computed.\\ Finally a
comparative look will be made to our results and those which have
been carried out by using other many body theories.
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