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Interference phenomenon for the Faddeevian regularization of 2D chiral fermionic determinants

1999; American Physical Society; Volume: 61; Issue: 2 Linguagem: Inglês

10.1103/physrevd.61.025014

1538-4500

Éverton M. C. Abreu, Anderson Ilha, C. Neves, C. Wotzasek,

Particle physics theoretical and experimental studies

The classification of the regularization ambiguity of a 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 find a new and important result that the Faddeevian class, with three second-class constraints, possesses 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-constraint class. We studied the restriction imposed by the interference of right-left modes of the chiral Schwinger model $(\ensuremath{\chi}{\mathrm{QED}}_{2})$ 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-constraint class which is the only nonambiguous class with a unique regularization parameter.