Boson-boson effective nonrelativistic potential for higher-derivative electromagnetic theories in D dimensions

TL;DR

This paper derives the effective nonrelativistic potential for charged scalar bosons in D-dimensional electromagnetism, revealing that while no bound states form in three dimensions without additional terms, bound states can exist with a Chern-Simons term.

Contribution

It provides a method to compute the effective potential in higher-dimensional electromagnetism and explores the conditions for boson-boson bound states, including the impact of topological terms.

Findings

No bound states in 3D without Chern-Simons term

Bound states exist in 3D with Chern-Simons term

Potential reduced to quadratures for arbitrary D

Abstract

The problem of computing the effective nonrelativistic potential $U_{D}$ for the interaction of charged scalar bosons within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that $U_3$ cannot bind a pair of identical charged scalar bosons; nevertheless, numerical calculations indicate that boson-boson bound states do exist in the framework of three-dimensional higher-derivative electromagnetism augmented by a topological Chern-Simons term.