Loop corrections and bosonization formulae

We study the functional integrals that appear in a path integral bosonizati on procedure for more than two spacetime dimensions. Since they are not in general exactly solvable, their evaluation by a suitable loop expansion cou ld be a natural procedure, even if the exact fermionic determinant were kno wn. The outcome of our study is that we can consistently ignore loop correc tions in the functional integral defining the bosonized action, if the same is done for the functional integral corresponding to the bosonic represent ation of the generating functional. IF contributions up to some order I in the number of loops are included in both integrals, all but the lowest term s cancel out in the final result for the generating functional. (C) 1999 Ac ademic Press.