One-Loop Determinant of Dirac Operator in Non-Renormalizable Models

TL;DR

This paper develops a proper-time regularization method to define the one-loop fermion determinant in non-renormalizable models, ensuring chiral invariance and symmetry preservation, exemplified through the NJL model.

Contribution

It introduces a modified polynomial correction to the fermion determinant that maintains chiral invariance in non-renormalizable models.

Findings

Proper-time regularization yields a chiral-invariant fermion determinant.

The method preserves fundamental symmetries in the NJL model.

The approach clarifies how to modify the fermion determinant for invariance.

Abstract

We use proper-time regularizations to define the one-loop fermion determinant in the form suggested by Gasser and Leutwyler some years ago. We show how to obtain the polynomial by which this definition of ln det D needs to be modified in order to arrive at the fermion determinant whose modulus is invarinat under chiral transformations. As an example it is shown how the fundamental symmetries associated with the NJL model are preserved in a consistent way.