The Global Minimum of the Effective Potential of the Many-Electron System with Delta-Interaction

Abstract

We 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.