Born-Infeld-Chern-Simons theory: Hamiltonian embedding, duality and bosonization

In this paper we study in detail the equivalence of the recently introduced Born-Infeld self-dual model to the Abelian Born-Infeld-Chern-Simons model in 2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme, to embed the Born-Infeld self-dual model to a gauge system and show that the embedded model is equivalent to Abelian Born-Infeld-Chern-Simons theory. Next, using Buscher's duality procedure, we demonstrate this equivalence in a covariant Lagrangian formulation and also derive the mapping between the n-point correlators of the (dual) field strength in Born-Infeld-Chern-Simons theory and of basic field in Born-Infeld self-dual model. Using this equivalence, the bosonization of a massive Dirac theory with a non-polynomial Thirring type current-current coupling, to leading order in (inverse) fermion mass is also discussed. We also rederive it using a master Lagrangian. Finally, the operator equivalence between the fermionic current and (dual) field strength of Born-Infeld-Chern-Simons theory is deduced at the level of correlators and using this the current-current commutators are obtained.