One-loop fermion determinant with explicit chiral symmetry breaking

We use a proper-time regularization to define the one-loop fermion determinant for the case in which explicit chiral symmetry breaking takes place. We show how to obtain the polynomial by which the standard definition of lndetD needs to be modified in order to arrive at the fermion determinant whose transformation properties are consistent with the general symmetry requirements of the basic Lagrangian. As an example it is shown how the fundamental symmetries and the explicit chiral symmetry breaking pattern associated with the ENJL model are preserved in a consistent way.