Stability of Matter in Magnetic Fields

TL;DR

This paper summarizes recent advances in understanding the stability of matter under strong magnetic fields and relativistic effects, clarifying the conditions for stability when magnetic fields and Dirac operators are involved.

Contribution

It provides a concise overview of recent results demonstrating stability criteria for matter in magnetic fields and relativistic regimes, resolving longstanding questions.

Findings

Magnetic fields do not destabilize matter when properly accounted for.

The Dirac operator with magnetic field preserves matter stability, unlike the free Dirac operator.

Stability depends on the choice of the negative energy sea filling prescription.

Abstract

The proof of the stability of matter is three decades old, but the question of stability when arbitrarily large magnetic fields are taken into account was settled only recently. Even more recent is the solution to the question of the stability of relativistic matter when the electron motion is governed by the Dirac operator (together with Dirac's prescription of filling the ``negative energy sea"). When magnetic fields are included the question arises whether it is better to fill the negative energy sea of the free Dirac operator or of the Dirac operator with magnetic field. The answer is found to be that the former prescription is unstable while the latter is stable. This paper is a brief, nontechnical summary of recent work with M. Loss, J.P. Solovej and H. Siedentop.