1 research outputs found
Bosonization in Higher Dimensions
Using the recently discovered connection between bosonization and duality
transformations (hep-th/9401105 and hep-th/9403173), we give an explicit
path-integral representation for the bosonization of a massive fermion coupled
to a U(1) gauge potential (such as electromagnetism) in d space (D=d+1
spacetime) dimensions. The bosonic theory is described by a rank d-1
antisymmetric Kalb-Ramond-type gauge potential. We construct the bosonized
lagrangian explicitly in the limit of large fermion mass. We find that the
resulting action is local for d=2 (and given by a Chern-Simons action), but
nonlocal for d larger than 3. By coupling to a statistical Chern-Simons field
for d=2, we obtain a bosonized formulation of anyons. The bosonic theory may be
further dualized to a theory involving purely scalars, for any d, and we show
this to be governed by a higher-derivative lagrangian for which the scalar
decouples from the U(1) gauge potential.Comment: (We had omitted some references and had misspelled `aficionados')
plain TeX, 11 pages, McGill-94/33, NEIP-94-006, OSLO-TP 10-9