Solvable Two-Dimensional Field Theory Based on Currents

Abstract

In this paper we study a solvable 2-dimensional field theory specified by a closed equal-time algebra generated by commutation of the components of the electric current and the energy-momentum tensor ${\theta }_{\mu \nu }$. As in the Thirring model, from which this model is abstracted, the physical content of the theory turns out to be trivial. The results are nevertheless of interest (a) because they allow one to readily understand why the Thirring model is solvable and why it has trivial physical consequences and (b) because they provide an example of a case where the requirement of a positive energy spectrum places important, and explicit, constraints on a theory written in terms of currents. We emphasize that although the present model was abstracted from the Thirring model we do not maintain that the resulting theory, or its solution as given here, is the same as the Thirring model, if by this term one means the conventional field-theoretic model.