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

Everton M. C. Abreu·Anderson Ilha·Clifford Neves·Clovis Wotzasek
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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 ($χQED_{2}$) 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.

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Everton M. C. Abreu, Anderson Ilha, Clifford Neves, Clovis Wotzasek. 2000-02-01. Interference Phenomenon for the Faddeevian Regularization of 2D Chiral Fermionic Determinants. https://doi.org/10.1103/physrevd.61.025014

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