On the Schr\"odinger-Born-Infeld system

TL;DR

This paper introduces a coupled Schr"odinger-Born-Infeld system modeling matter-electromagnetic interactions, using variational methods to find electrostatic ground states, offering a novel dualistic framework beyond classical Maxwell theory.

Contribution

It proposes a new coupled system based on Schr"odinger and Born-Infeld Lagrangians and demonstrates the existence of electrostatic ground state solutions through variational analysis.

Findings

Existence of electrostatic radial ground state solutions.

Development of variational estimates for the coupled system.

A dualistic model replacing classical Maxwell electromagnetism.

Abstract

In this paper we study a system which we propose as a model to describe the interaction between matter and electromagnetic field from a dualistic point of view. This system arises from a suitable coupling of the Schr\"odinger and the Born-Infeld lagrangians, this latter replacing the role that, classically, is played by the Maxwell lagrangian. We use a variational approach to find an electrostatic radial ground state solution by means of suitable estimates on the functional of the action.