Abstract
Abstract We consider the solitonic sector of the SU(2) Nambu-Jona-Lasinio model with vector mesons. We prove that none of the previously proposed procedures to handle the fermion determinant reproduces the perturbative expansion in the vector coupling constant. Hence they are either not consistent with the way the parameters of the model are fixed in the meson sector or they violate Lorentz invariance of the vacuum. We propose a new prescription at the operator level both in the proper-time and the Pauli-Villars regularization. Our method is in accordance with perturbation theory, explicitly preserves vector gauge invariance and allows for a consistent treatment of the meson and the soliton sector. The convergence radius of the perturbative expansion is also studied. We also show how direct calculations in Minkowski space might be performed.
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