Determine the critical stability and collapse couplings

Determine the critical couplings separating stability from collapse for the Pauli and relativistic spinless non-Abelian gauge-field models, and likewise clarify the corresponding critical couplings in the abelian case.

Background

The paper proves stability below explicit small-coupling thresholds and collapse above substantially larger thresholds for both the Pauli and relativistic spinless models. Consequently, the proven regimes leave wide gaps in the coupling constant.

The unresolved issue is to identify the actual critical couplings. In the Pauli case, the authors relate this question to the field strength required to support a Pauli zero mode.