Noncommutativity in Maxwell-Chern-Simons-Matter Theory Simulates Pauli Magnetic Coupling

Abstract

We study interactions between like charges in the noncommutative Maxwell-Chern-Simons electrodynamics {\it{minimally}} coupled to spinors or scalars. We demonstrate that the non-relativistic potential profiles, for only spatial noncommutativity, are nearly identical to the ones generated by a {\it{non-minimal}} Pauli magnetic coupling, originally introduced by Stern \cite{js}. Although the Pauli term has crucial roles in the context of physically relevant objects such as anyons and like-charge bound states (or "Cooper pairs"), its inception \cite{js} (see also \cite{others}) was ad-hoc and phenomenological in nature. On the other hand we recover similar results by extending the minimal model to the noncommutative plane, which has developed in to an important generalization to ordinary spacetime in recent years. No additional input is needed besides the noncommutativity parameter. We prove a novel result that for complex scalar matter sector, the bound states (or "Cooper pairs" can be generated {\it{only}} if the Maxwell-Chern-Simons-scalar theory is embedded in noncommutative spacetime. This is all the more interesting since the Chern-Simons term does not directly contribute a noncommutative correction term in the action.