2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58231We prove that the global minimum of the real part of the full effective potential of the many-electron system with attractive delta-interaction is in fact given by the BCS mean field configuration. This is a consequence of a simple bound which is obtained by applying Hadamard's inequality to the functional determinant. The second order Taylor expansion around the minimum is computed.18 pages, TeXMathematical PhysicsStatistical Mechanics81T10; 81V70; 82D55; 81T08text