Two-dimensional Yukawa interaction driven by a nonlocal-Proca quantum electrodynamics

TL;DR

This paper derives effective (2+1)D models for Yukawa interactions among Dirac electrons, incorporating nonlocal-Proca quantum electrodynamics with gauge invariance, and calculates one-loop mass renormalization, extending the framework of PQED.

Contribution

It introduces a novel nonlocal-Proca QED model for Yukawa interactions in reduced dimensions, preserving gauge invariance and generalizing PQED for new applications.

Findings

Reproduces Yukawa potential in static limit

Calculates one-loop mass renormalization

Extends PQED to Yukawa interactions

Abstract

We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle, which may be either scalar or an abelian gauge field, both of them in (3+1) dimensions. Thereafter, we consider that the matter field propagates only in (2+1) dimensions, whereas the bosonic field is free to propagate out of the plane. Within these assumptions, we apply a mechanism for dimensional reduction, which yields an effective model in (2+1) dimensions. In particular, for the gauge-field case, we use the Stueckelberg mechanism in order to preserve gauge invariance. We refer to this version as nonlocal-Proca quantum electrodynamics (NPQED). For both scalar and gauge cases, the effective models reproduce the usual $e^{-m r}/r$ Yukawa interaction in the static limit. By means of perturbation theory at one loop, we calculate the mass renormalization of the Dirac field. Our model is a generalization of Pseudoquantum electrodynamics (PQED), which is a gauge-field model that provides a Coulomb interaction for two-dimensional electrons. Possibilities of application to Fermi-Bose mixtures in mixed dimensions, using cold atoms, are briefly discussed.