Quantum electrodynamics and the electron self-energy in a deformed space with a minimal length scale

TL;DR

This paper develops a quantum electrodynamics framework incorporating a minimal length scale to address divergences, deriving regularized propagators and self-energy corrections within this novel setting.

Contribution

It introduces a new QED framework with a minimal length, providing regularized propagators and analyzing divergence removal compared to traditional theories.

Findings

Scalar field mass regularized by minimal length

Electron and photon propagators derived with minimal length effects

Electron self-energy computed as a function of minimal length

Abstract

The main motivation to study models in the presence of a minimal length is to obtain a quantum field theory free of the divergences. In this way, in this paper, we have constructed a new framework for quantum electrodynamics embedded in a minimal length scale background. New operators are introduced and the Green function method was used for the solution of the field equations, i.e., the Maxwell, Klein-Gordon and Dirac equations. We have analyzed specifically the scalar field and its one loop propagator. The mass of the scalar field regularized by the minimal length was obtained. The QED Lagrangian containing a minimal length was also constructed and the divergences were analyzed. The electron and photon propagators, and the electron self-energy at one loop as a function of the minimal length was also obtained.