Canonical approach to 2D WZNW model, non-abelian bosonization and anomalies

TL;DR

This paper develops a canonical framework for the 2D WZNW model, deriving non-abelian bosonization rules and anomalies, linking classical constraints to quantum operator algebra.

Contribution

It presents a canonical derivation of non-abelian bosonization and anomaly expressions in the 2D WZNW model, connecting classical and quantum formalisms.

Findings

Derived the effective action with isomorphic Poisson and operator algebras.

Obtained non-abelian bosonization rules for currents and densities.

Expressed anomalies as functions of the Schwinger term using canonical methods.

Abstract

The gauged WZNW model has been derived as an effective action, whose Poisson bracket algebra of the constraints is isomorphic to the commutator algebra of operators in quantized fermionic theory. As a consequence, the hamiltonian as well as usual lagrangian non-abelian bosonization rules have been obtained, for the chiral currents and for the chiral densities. The expression for the anomaly has been obtained as a function of the Schwinger term, using canonical methods.