Relativistic potential of a hydrogen-like system in Poincare invariant quantum mechanics

TL;DR

This paper develops a Poincare-covariant model for a relativistic hydrogen-like atom, deriving a gauge-invariant potential kernel to accurately describe the electromagnetic interaction between two fermions.

Contribution

It introduces a novel Poincare-invariant framework with a gauge-invariant potential kernel for relativistic two-fermion systems, advancing the theoretical modeling of hydrogen-like atoms.

Findings

Derived the radial integral equation kernel for the system.

Established a gauge-invariant potential for relativistic two-fermion interactions.

Provided a foundation for more accurate relativistic atomic models.

Abstract

To describe a relativistic hydrogen atom we used the Poincare-covariant model of a two particle system with gauge invariant potential. The kernel of the radial integral equation is obtained which describes a system of two fermions with electromagnetic interaction.