Extended Dualization: a method for the Bosonization of Anomalous Fermion Systems in Arbitrary Dimension

Abstract

The technique of extended dualization developed in this paper is used to bosonize quantized fermion systems in arbitrary dimension $D$ in the low energy regime. In its original (minimal) form, dualization is restricted to models wherein it is possible to define a dynamical quantized conserved charge. We generalize the usual dualization prescription to include systems with dynamical non--conserved quantum currents. Bosonization based on this extended dualization requires the introduction of an additional rank $0$ (scalar) field together with the usual antisymmetric tensor field of rank $(D-2)$. Our generalized dualization prescription permits one to clearly distinguish the arbitrariness in the bosonization from the arbitrariness in the quantization of the system. We study the bosonization of four--fermion interactions with large mass in arbitrary dimension. First, we observe that dualization permits one to formally bosonize these models by invoking the bosonization of the free massive Dirac fermion and adding some extra model--dependent bosonic terms. Secondly, we explore the potential of extended dualization by considering the particular case of \underbar{chiral} four--fermion interactions. Here minimal dualization is inadequate for calculating the extra bosonic terms. We demonstrate the utility of extended dualization by successfully completing the bosonization of this chiral model. Finally, we consider two examples in two dimensions which illuminate the utility of using extended dualization by showing how quantization ambiguities in a fermionic theory propagate into the bosonized version. An explicit parametrization of the quantization ambiguities of the chiral current in the Chiral Schwinger model is obtained. Similarly, for the sine--Gordon interaction in the massive Thirring model the quantization