Consequence of local U(1)VxU(1)A symmetry in two dimensions

We study the two-dimensional U(1)VxU(1)A model in detail. This model has both local vector U(1) and local axial-vector U(1) gauge symmetries. The original Lagrangian is expressed in terms of some fermion fields and a gauge field. We bosonize fermion fields by the same method as in the Thirring model. The U(1)VxU(1)A symmetry requires the vanishing of the Schwinger term (or, equivalently, the nilpotency of the Becchi-Rouet-Stora-Tyutin charge). The absence of the Schwinger term leads to some negative-norm states (ghost fields). However, the physical states are positive semidefinite if and only if the number of ghost fields is only one. We show the no-ghost theorem in detail