Interference Phenomenon for the Faddeevian Regularization of 2D Chiral Fermionic Determinants

TL;DR

This paper classifies regularization ambiguities in 2D fermionic determinants, introduces a new Faddeevian class with a continuous parameter, and shows interference effects restrict regularization choices to a unique class.

Contribution

It extends the classification of 2D fermionic determinant regularizations to include a new Faddeevian class with a continuous parameter and analyzes interference effects in chiral QED2.

Findings

Faddeevian class has a continuous parameter family.

Unitarity restricts the parameter range.

Interference effects select a unique regularization class.

Abstract

The classification of the regularization ambiguity of 2D fermionic determinant in three different classes according to the number of second-class constraints, including the new faddeevian regularization, is examined and extended. We found a new and important result that the faddeevian class, with three second-class constraints, possess a free continuous one parameter family of elements. The criterion of unitarity restricts the parameter to the same range found earlier by Jackiw and Rajaraman for the two-constraints class. We studied the restriction imposed by the interference of right-left modes of the chiral Schwinger model ($\chi QED_{2}$) using Stone's soldering formalism. The interference effects between right and left movers, producing the massive vectorial photon, are shown to constrain the regularization parameter to belong to the four-constraints class which is the only non-ambiguous class with a unique regularization parameter.