Complete solution of the chiral Schwinger model Hilbert space, constraints and Wess-Zumino terms

Abstract

The chiral Schwinger model is completely solved by bosonization. The Hilbert space is constructed and it is found to be of indefinite metric. The quantum constraints that define the physical subspace are determined and the physical operators (those that commute with the constraints) are found. We compute their correlation functions and find that there is non-trivial fermion wave function renormalization constant (Z2) and vertex renormalization constant (Z1−) and that Z2 = Z1 although the theory has lost its gauge invariance because of the chiral anomaly.The addition of a Wess-Zumino (WZ) term is studied and the modifications of the constraints introduced by this term is analyzed. The physical gauge invariant correlation functions in the theory with the WZ term are found to be the same as the physical correlation functions of the theory without the WZ terms.