BOSONIZATION IN HIGHER DIMENSIONS

Using the recently discovered connection between bosonization and dual ity transformations, we give an explicit path-integral representation for the bosonization of a massive fermion coupled to a U(1) gauge pote ntial (such as electromagnetism) in d greater than or equal to 2 space (D = d + 1 greater than or equal to 3 spacetime) dimensions. We perfo rm this integral explicitly in the limit of large fermion mass. We fin d that the bosonic theory is described by a rank d - 1 antisymmetric K alb-Ramond-type gauge potential, whose action is local for d = 2 (give n by a Chem-Simons action), but nonlocal for d greater than or equal t o 3. By coupling to a statistical Chem-Simons held for d = 2, we obtai n 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 a higher-derivative theory for which the scalar decouples from the U(1) gauge potential.