Stability of a single species of identical bosons

Establish whether the non-relativistic $SU(2)$ colour-charged Schrödinger Hamiltonian for a single species of identical bosons satisfies a stability-of-the-second-kind bound of the form $-CN$.

Background

The paper proves instability of order N7/5N^{7/5} for two bosonic species by using colour-up and colour-down states to reproduce the attractive two-component charged Bose gas. That construction does not resolve the one-species problem.

For one species, Bose symmetry constrains the available colour and spatial channels: without additional internal labels, the attractive colour-singlet channel requires an antisymmetric spatial pair state, while condensate states occupy the repulsive triplet channel. The authors therefore leave stability versus instability unresolved.

References

For a single species of identical bosons, stability of the second kind is open (Remark~\ref{rem:bosons}).

— Stability of Matter Interacting with Classical Non-Abelian Gauge Fields  (2610.08313 - Reuvers et al., 6 Oct 2026) in Section 'Open problems', item 4; see also Remark 'Bosons'

The analogous problem with a quantized colour field, with an ultraviolet cutoff, is open.

— Stability of Matter Interacting with Classical Non-Abelian Gauge Fields  (2610.08313 - Reuvers et al., 6 Oct 2026) in Section 'Open problems', item 5