Instability of a Pseudo-Relativistic Model of Matter with Self-Generated Magnetic Field

TL;DR

This paper demonstrates that in a pseudo-relativistic matter model, incorporating self-generated magnetic fields causes instability regardless of the method of interaction, highlighting fundamental limitations of the model.

Contribution

It proves the universal instability of a pseudo-relativistic matter model with self-generated magnetic fields for all positive fine structure constants.

Findings

Inclusion of self-generated magnetic fields leads to instability.

Instability occurs regardless of the magnetic interaction method.

Results hold for all positive fine structure constants.

Abstract

For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all positive values of the fine structure constant. This is true no matter whether this interaction is accounted for by the Breit potential, by an external magnetic field which is chosen to minimize the energy, or by the quantized radiation field.