One-loop determinant of Dirac operator in non-renormalizable models

We use proper-time regularizations to define the one-loop fermion determina nt in the form suggested by Gasser and Leutwyler some years ago, We show ho w to obtain the polynomial by which this definition of In det D needs to be modified in order to arrive at the fermion determinant whose modulus is in variant under chiral transformations. As an example it is shown how the fun damental symmetries associated with the NJL model are preserved in a consis tent way. (C) 2000 Elsevier Science B.V, AU rights reserved.