ANALYTICAL CONTINUATION OF THE FERMION DETERMINANT WITH A FINITE CUTOFF

We consider the solitonic sector of the SU(2) Nambu-Jona-Lasinio model with vector mesons. We prove that none of the previously proposed pro cedures to handle the fermion determinant reproduces the perturbative expansion in the vector coupling constant. Hence they are either not c onsistent with the way the parameters of the model are fixed in the me son sector or they violate Lorentz invariance of the vacuum. We propos e a new prescription at the operator level both in the proper-time and the Pauli-Villars regularization. Our method is in accordance with pe rturbation theory, explicitly preserves vector gauge invariance and al lows for a consistent treatment of the meson and the soliton sector. T he convergence radius of the perturbative expansion is also studied. W e also show how direct calculations in Minkowski space might be perfor med.