Ground state degeneracy of the Pauli-Fierz Hamiltonian inlcuding spin

TL;DR

This paper proves that for a spin-1/2 electron minimally coupled to the quantized radiation field, the ground state degeneracy is two-fold for small charge and momentum, with specific angular momentum properties.

Contribution

It establishes the two-fold degeneracy of the ground state in the Pauli-Fierz model including spin and analyzes angular momentum characteristics.

Findings

Ground state subspace is two-fold degenerate for small charge and momentum.

Total angular momentum of the ground state is ±1/2.

Results extend to cases with confining external potentials.

Abstract

We consider an electron, spin 1/2, minimally coupled to the quantized radiation field in the nonrelativistic approximation, a situation defined by the Pauli-Fierz Hamiltonian $H$. There is no external potential and $H$ fibers as $\int^\oplus H_p dp$ according to the total momentum $p$. We prove that the ground state subspace of $H_p$ is two-fold degenerate provided the charge $e$ and the total momentum $p$ are sufficiently small. We also establish that the total angular momentum of the ground state subspace is $\pm1/2$ and study the case of a confining external potential.