Bosonization and Duality of Massive Thirring Model

Starting from a formulation of the Thirring model as a gauge theory, we consider the bosonization of the D-dimensional massive Thirring model (D \\ge 2) with four-fermion interaction of the current-current type. Especially we pay attention to the case of very massive fermion m \\gg 1 in (2+1) and (1+1) dimensions. Up to the next-to-leading order of 1/m, we show that the (2+1)-dimensional massive Thirring model is mapped to the Maxwell-Chern-Simons theory and that the (1+1)-dimensional massive Thirring model is equivalent to the massive free scalar field theory. In the process of the bosonization of the Thirring model, we point out the importance of the gauge-invariant formulation.