On Bosonization Ambiguities of Two Dimensional Quantum Electrodynamics
  We study bosonization ambiguities in two dimensional quantum electrodynamics in the presence and in the absence of topologically charged gauge fields. The computation of fermionic correlation functions suggests that ambiguities may be absent in nontrivial topologies, provided that we do not allow changes of sector as we evaluate functional integrals. This would remove an infinite arbitrariness from the theory. In the case of trivial topologies, we find upper and lower bounds for the Jackiw-Rajaraman parameter, corresponding to the limiting cases of regularizations which preserve gauge or chiral symmetry. 
S. A. Dias and M. B. Silva Neto