The thermodynamic limit for matter interacting with Coulomb forces and with the quantized electromagnetic field: I. The lower bound

TL;DR

This paper advances the understanding of the thermodynamic limit in quantum electrodynamics by establishing a lower bound on free energy that accounts for magnetic and quantized electromagnetic interactions.

Contribution

It provides a new lower bound for free energy in non-relativistic QED, incorporating magnetic fields and the quantized electromagnetic field, extending previous results on matter stability.

Findings

Established a proportional lower bound on free energy with particle number

Accounted for magnetic and electromagnetic quantum effects

Extended thermodynamic limit proofs to include QED interactions

Abstract

The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, in the framework of non-relativistic quantum mechanics, was accomplished decades ago. This result did not take account of interactions caused by magnetic fields, however, (the spin-spin interaction, in particular) or of the quantized nature of the electromagnetic field. Recent progress has made it possible to undertake such a proof in the context of non-relativistic QED. This paper contains one part of such a proof by giving a lower bound to the free energy which is proportional to the number of particles and which takes account of the fact that the field, unlike the particles, is never confined to a finite volume. In the earlier proof the lower bound was a `two line' corollary of the `stability of matter'. In QED the proof is much more complicated.