Consequence of local U(1)V x U(1)A symmetry in two dimensions.

Abstract

We study the two-dimensional U(1){sub {ital V}}{times}U(1){sub {ital 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){sub {ital V}}{times}U(1){sub {ital 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.