CHIRAL BOSONIZED ACTION AND THE MINIMAL WESS-ZUMINO-WITTEN ACTION FOR CHIRAL TWO-DIMENSIONAL QCD FROM PATH-INTEGRAL METHOD

Abstract

The path-integral method is applied to derive the chiral bosonized action and the minimal WZW action for chiral QCD2. An interesting feature in our model is that the Poisson brackets of the new set of constraints, which is a recombination of the original ones, are field-independent on the constraint surface. The correct contribution from det {Ωi, Ωj} or δ(Ωa) is considered, and it seems to affect the properties of the integration measure. Here Ωi are the original chiral constraints, Ωa are linear combination of Ωi. However, due to the determinants of Lab(ɸ) and [Formula: see text] (the definition of Lab(ɸ) and [Formula: see text] can be seen from Eqs. (22) and (41)) being ±1, the right-invariant measure is equivalent to the left-invariant measure, which is quite unlike the case of the gauge quasigroup. As a result, we can identify the integration measure in our model with the Haar measure.