Stability with static colour-neutral nuclei for Pauli and relativistic matter

Establish stability, for small couplings, of the Pauli and relativistic spinless Hamiltonians describing colour-charged particles in the presence of static colour-neutral nuclei coupled through an additional abelian field.

Background

The paper sketches a model with gauge group $SU(2)\times U(1)$, dynamical colour-charged particles, and static nuclei carrying only abelian charge. Stability of the spinless Schrödinger Hamiltonian is argued to persist uniformly in the fields and nuclear positions for all couplings.

For the Pauli and relativistic Hamiltonians, the reduction leads to corresponding abelian stability problems with static nuclei but with a non-abelian kinetic operator. The authors expect the existing methods to extend, but do not establish the required details.