Commuting Quantum Matrix Models

Understand

We study a quantum system of $p$ commuting matrices and find that such a quantum system requires an explicit curvature dependent potential in its Lagrangian for the system to have a finite energy ground state.

• In contrast it is possible to avoid such curvature dependence in the Hamiltonian.
• We study the eigenvalue distribution for such systems in the large matrix size limit.
• A critical r\^ole is played by $p=4$.