Abstract
Approximate but reliable solutions of a quantum system with N identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary kinematics and one- or two-body potentials. It is adapted here for cyclic systems with N identical particles, that is to say systems in which a particle i has only an interaction with particles i-1 and i+1 (with N+1≡ 1).