Effective theories and non-minimal couplings in low-dimensional systems

TL;DR

This paper explores non-minimal electromagnetic couplings in low-dimensional systems, using transformations and dimensional reduction to analyze interactions for bosonic and fermionic fields in various electromagnetic theories.

Contribution

It introduces a detailed analysis of non-minimal couplings in 3D and 4D systems, including dimensional reduction and comparison of different electromagnetic models.

Findings

Non-minimal couplings analyzed via Foldy-Wouthuysen transformation.

Dimensional reduction from 4D to 3D reproduces known scenarios.

Comparison between Maxwell and Maxwell-Chern-Simons electrodynamics.

Abstract

Dimensionality aspects of non-minimal electromagnetic couplings are investigated. By means of the Foldy-Wouthuysen transformation, we attain (non-)relativistic interactions related to the non-minimal coupling in three-dimensional spacetime, for both the bosonic and fermionic fields. Next, we establish some comparisons and analyse particular situations in which the external electromagnetic fields are described either by Maxwell or Maxwell-Chern-Simons Electrodynamics. In addition, we consider the situation of a non-minimal coupling for the fermionic field in four dimensions, carry out its dimensional reduction to three dimensions and show that the three-dimensional scenario previously worked out can be recovered as a particular case. Finally, we discuss a number of structural aspects of both procedures.