Semiclassical expansion of the ground state for a model of interacting spins in QED

TL;DR

This paper derives asymptotic expansions for the ground state and energy of a quantum electrodynamics model with interacting spins, providing insights into magnetic properties and radiative corrections.

Contribution

It introduces new asymptotic expansion techniques for the ground state and energy in a spin-QED system, including a first-order radiative correction.

Findings

Asymptotic formulas for ground state energy and magnetic field

First-order radiative correction computed

Elementary formulas recovered from expansions

Abstract

In this article, we consider fixed spin 1/2 particles interacting through the quantized electromagnetic field in a constant magnetic field. We give some asymptotic expansions for the ground state and the ground state energy of the Hamiltonian operator $H(h)$ describing this system. The first terms of these expansions enable to recover elementary formulas for the energy and the magnetic field of the spins when considered as magnets. A first order radiative correction is computed for the energy.